Turito Academy

Test Prep

Global form fields

The given equation <img src="data:image/png;base64,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" class="Wirisformula" alt="fraction numerator d y over denominator d x end fraction plus fraction numerator y over denominator x end fraction equals x to the power of 2 end exponent" width="101" height="35" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mfrac»«mrow»«mi»d«/mi»«mi»y«/mi»«/mrow»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mo»+«/mo»«mfrac»«mrow»«mi»y«/mi»«/mrow»«mrow»«mi»x«/mi»«/mrow»«/mfrac»«mo»=«/mo»«msup»«mrow»«mi»x«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«/math»'/>is of the form <img src="data:image/png;base64,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" class="Wirisformula" alt="fraction numerator d y over denominator d x end fraction plus P y equals Q" width="94" height="35" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mfrac»«mrow»«mi»d«/mi»«mi»y«/mi»«/mrow»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mo»+«/mo»«mi»P«/mi»«mi»y«/mi»«mo»=«/mo»«mi»Q«/mi»«/math»'/>. So, I.F.= <img src="data:image/png;base64,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" class="Wirisformula" alt="e to the power of not stretchy integral fraction numerator 1 over denominator x end fraction d x end exponent equals e to the power of log invisible function application x end exponent equals x" width="132" height="32" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«msup»«mrow»«mi»e«/mi»«/mrow»«mrow»«mrow»«mo stretchy=¨false¨»∫«/mo»«mrow»«mfrac»«mrow»«mn»1«/mn»«/mrow»«mrow»«mi»x«/mi»«/mrow»«/mfrac»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mrow»«/mrow»«/msup»«mo»=«/mo»«msup»«mrow»«mi»e«/mi»«/mrow»«mrow»«mrow»«mrow»«mi»log«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mi»x«/mi»«/mrow»«/mrow»«/mrow»«/msup»«mo»=«/mo»«mi»x«/mi»«/math»'/> Hence required solution <img src="data:image/png;base64,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" class="Wirisformula" alt="x y equals not stretchy integral x. x to the power of 2 end exponent d x plus c" width="134" height="31" style="vertical-align:-9px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»x«/mi»«mi»y«/mi»«mo»=«/mo»«mrow»«mo stretchy=¨false¨»∫«/mo»«mrow»«mi»x«/mi»«mo».«/mo»«msup»«mrow»«mi»x«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«mi»d«/mi»«mi»x«/mi»«mo»+«/mo»«mi»c«/mi»«/mrow»«/mrow»«/math»'/> Þ <img src="data:image/png;base64,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" class="Wirisformula" alt="x y equals fraction numerator x to the power of 4 end exponent over denominator 4 end fraction plus c" width="89" height="39" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»x«/mi»«mi»y«/mi»«mo»=«/mo»«mfrac»«mrow»«msup»«mrow»«mi»x«/mi»«/mrow»«mrow»«mn»4«/mn»«/mrow»«/msup»«/mrow»«mrow»«mn»4«/mn»«/mrow»«/mfrac»«mo»+«/mo»«mi»c«/mi»«/math»'/> Þ <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFsAAAATCAYAAAD/PXGYAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAAdpJREFUeNpjYBiZIBqI/zOMApoDHSA+OhrYtAeCQHwciKVHA5v2YA0QW0LZgyawfYZhzJcDcSwSf1D4jweIrw3DwP6PAw8omAnEySOgTPtPI7VEA2sg3kvAAlBEdGARb4bKgcBcIA7HoqYAiFup7GZi3EPvwAaVDl1A/BSIfwHxOmjlDAdsQHwJiOWJsOAcEIsj8ROBeAoSPx5qGTLgAuJbQCxMQhYnNrsTcg89A5sH6h5QouKDhmsJtB6EA1DqyCHSAg8g7oOyXZByAwx4AfEqNLF6IK6lUZFAyD30LHJA4TgJnwI9aEOfFAt2A7E9EF/AklpB/CtIfFEgvgvEHDQsg/G5h1qVKaGcxgTEr9GLDHRwEohVSAzsAmh5pIdD/hsSuw+qntqeI8U99EjZpkB8mNKYxFaRroEGYiQOM0GWKkHxXWis0woQ4x56BLYXtDKkmgWgwNsErfBAlcEZHNl2IRD7AfFStM4EtQGx7qFHYBsD8Q1qWQAqe7eheQZUyy7Gka3nQls4tAKkuIdeFeQFaEuEBdoaKYDmPJIsYINmEWksapdDWwTIIABqhh+NAppU99ALyALxQSD+A01oyfSwFBTIxxlGAV0AKHtbjgYD7QFogH7LaDCgAgAOAZI0iDONkwAAAJx0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bW4+NDwvbW4+PG1pPng8L21pPjxtaT55PC9taT48bW8+PTwvbW8+PG1zdXA+PG1pPng8L21pPjxtbj40PC9tbj48L21zdXA+PG1vPis8L21vPjxtaT5jPC9taT48L21hdGg+sEljEAAAAABJRU5ErkJggg==" class="Wirisformula" alt="4 x y equals x to the power of 4 end exponent plus c" width="91" height="19" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mn»4«/mn»«mi»x«/mi»«mi»y«/mi»«mo»=«/mo»«msup»«mrow»«mi»x«/mi»«/mrow»«mrow»«mn»4«/mn»«/mrow»«/msup»«mo»+«/mo»«mi»c«/mi»«/math»'/>.

The solution of the differential equation <img src="data:image/png;base64,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" class="Wirisformula" alt="fraction numerator d y over denominator d x end fraction plus fraction numerator y over denominator x end fraction equals x to the power of 2 end exponent" width="101" height="35" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mfrac»«mrow»«mi»d«/mi»«mi»y«/mi»«/mrow»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mo»+«/mo»«mfrac»«mrow»«mi»y«/mi»«/mrow»«mrow»«mi»x«/mi»«/mrow»«/mfrac»«mo»=«/mo»«msup»«mrow»«mi»x«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«/math»'/> is

Solution for the question - the solution of the differential equation (dy)/(dx)+(y)/(x)=x^(2) is xy=4x^(4)+c '/>   (1)/(4)xy=x^(4)+c '/>   xy=x^(4)+c '/>

The solution of the differential equation (dy)/(dx)+(y)/(x)=x^(-Turito

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Solution of differential equation <img src="data:image/png;base64,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" class="Wirisformula" alt="fraction numerator d y over denominator d x end fraction equals fraction numerator y minus x over denominator y plus x end fraction" width="91" height="38" style="vertical-align:-15px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mfrac»«mrow»«mi»d«/mi»«mi»y«/mi»«/mrow»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mi»y«/mi»«mo»-«/mo»«mi»x«/mi»«/mrow»«mrow»«mi»y«/mi»«mo»+«/mo»«mi»x«/mi»«/mrow»«/mfrac»«/math»'/> is

Solution for the question - solution of differential equation (dy)/(dx)=(y-x)/(y+x) is y=x-2log_(e)y+c '/>   (1+(x)/(y))y=(1-(x)/(y))x+c '/>  (y^(2))/(2)+xy=xy-(x^(2))/(2)+c '/>

Solution of differential equation (dy)/(dx)=(y-x)/(y+x) is -Turito

The solution of the equation <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGUAAAAmCAYAAADdsFUNAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAApJJREFUeNrtmjFIHEEUhheRIEGEIGJxRUAsJIgIKYJYiBBEJBxiE0KQIIK1XapwhQhicYWkkyMECQeHSJDDRkREQgiEEERSCFaSNoiFSJrL/7i3MAyrt5vbm3s7vh8+2J25hdk3O29mbv4g+H9dg45AJUaD4ETDIEuzoKxhaJ+6wQa4BDdgG7wHb7m+BF5GPLcMVjP83otgLaJ8hevaJpozDsECX/eAAqjxaCG9AevWcw/BGejN+Af5A/Qb9wv8QbZV74wRYYoCnuPrGVCx6gv8bNY1DYp8/RwcSGjUBacve/RcG/c0Gk6N+z5wDro8Sd/7YAL8lDDyR8FRRPkzTmn28jhUkecTX0Tv8heMSGjMHNiKKH8FPlhlx2CAOfdo/zLOC5siv7eIZW8lopw6askq+wjy4BOY96RD6APb5UULpfDvEtIXNeYXpzHSU1AFv3lyt4d4yaMNJc2Le1YnvLglczgXLQd3eH/yFUyCPxGT+Cwvk/MedMgDfudcRF2ZV2SZUJ47TSVINNTHNAxyNMxzjcoz1WKgUmXna22WrLa7luH4aPpSqVQqlcoHSbUXhX+1XwX1MxA6mHp9HzpEsr2IDuXo3CM8LX0CvgRCzkJaqazZix4HnnnUGtmLSGKtOIZurHuXtqhU4xPHXhRKpBWHNcYpzJRrW1Rq8YljLwol0ooT1A/jvvECwJRrW1Rq8YljLzIlyooDPQKfwVREXVJbVBp/AzUdnyT2IjMfS7HiDHCHDDZY1odyYYtqOj5J7EXm/kCCFWcIbPIccZdc2qJSiU8Se5EkK04/t7szxm9d2aJSi09ce5E0K06VR0rcdNJqW1Tq8WlkL5JoxUkyEbfaFuWNVcml1BYlUGqLEibRtqh/GBIJlZCNnW4AAADodEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1mcmFjPjxtcm93PjxtaT5kPC9taT48bWk+eTwvbWk+PC9tcm93Pjxtcm93PjxtaT5kPC9taT48bWk+eDwvbWk+PC9tcm93PjwvbWZyYWM+PG1vPj08L21vPjxtZnJhYz48bWk+eDwvbWk+PG1yb3c+PG1uPjI8L21uPjxtaT55PC9taT48bW8+LTwvbW8+PG1pPng8L21pPjwvbXJvdz48L21mcmFjPjwvbWF0aD4CL4xMAAAAAElFTkSuQmCC" class="Wirisformula" alt="fraction numerator d y over denominator d x end fraction equals fraction numerator x over denominator 2 y minus x end fraction" width="101" height="38" style="vertical-align:-15px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mfrac»«mrow»«mi»d«/mi»«mi»y«/mi»«/mrow»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mi»x«/mi»«/mrow»«mrow»«mn»2«/mn»«mi»y«/mi»«mo»-«/mo»«mi»x«/mi»«/mrow»«/mfrac»«/math»'/> is

Solution for the question - the solution of the equation (dy)/(dx)=(x)/(2y-x) is y=(x)/(2y-x)+c '/>   y=(2y-x)+c '/>   y=x+c '/>  (x-y)(x+2y)^(2)=c '/>

The solution of the equation (dy)/(dx)=(x)/(2y-x) is -Turito

The solution of the differential equation <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGsAAAApCAYAAAAyL9drAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAArpJREFUeNrtmjFIHEEUhpcUEkKwERG57pBgISJYSEgRAilE5DjSBAsRCVhYpUslVwQhpLhCbI8QJByIpAjBRkIQERsREbEIWElaSXUcNvF/d+9kGcbbmdu9cWZ2PvjhdvYW3puZfTO7+0dR7zSgR1HAesags9ANblCG6qEb7OMptAH9g5rQDrQJfeDzNeit5Lr30LqjOb+DPknaP/I5K/OmNek3tMy/B6EK9J/vLmIJ+ixc9wT6Aw05PElPoJHY8TJP0sjWvNdid1AcCqjAv+egbeF8ha91mVmoyr9fQ7+E89blfcVlULzbGrFjmkXnseNh6BJ67MESsAe9hE4ld4tVeU9B+5L2GS6N4ja+Q5Xrtg9QHjfQZJfHFyvyfgNtSdoXoC9C2wFUZF168vz1gjdTVc5ZhjV5lyU1OeIBXBHavkIl6Bu06MFAUef/4A0DLQPH92warMmbAr3gckhMQz+hv7y4iuWi5smDMq09u8LgzN9TZazKm7au3/n56gh6BV1LFtEyb+dLjg/UAOdbkJyr8w7R+bxLPJh5w8m8qWw8z+FgOZf3BK9leSOvebfqfpICAX9nd1q5GvdDK5TBQCAQCAQc21DRJ5DDqG0C8jIOn2xolMdq1P6M710cvtrQmj7G4aMNjT7d77seR5INjVCxbdnMKK8VRZfjULGhdUiybdnKs6j9MnbU9ThUbGgdkmxbtt5RuzwJe9nB2RDHHSo2tDjdbFsmUS3L1EHjKbbbKqi4dtPE0ULHhhYPoJttyyQqZTnN+0fV/6q4dlO/B9WxoREqti2T9Lssq3aoEdeujg1N1bZlmizLcq9fBYy4dlVtaDq2LdP0syzrlCojrt0kG5qubcsk/S7LOoPlo1s5M0yUZZ3B8s2tnBmmyrLOYPnkVs4MW8uyL27lXJBXt7KT5NWt7ByZunZvATWjNQEIqR3HAAABI3RFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtZnJhYz48bXJvdz48bWk+ZDwvbWk+PG1pPnk8L21pPjwvbXJvdz48bXJvdz48bWk+ZDwvbWk+PG1pPng8L21pPjwvbXJvdz48L21mcmFjPjxtbz49PC9tbz48bWZyYWM+PG1yb3c+PG1pPng8L21pPjxtaT55PC9taT48L21yb3c+PG1yb3c+PG1zdXA+PG1pPng8L21pPjxtbj4yPC9tbj48L21zdXA+PG1vPis8L21vPjxtc3VwPjxtaT55PC9taT48bW4+MjwvbW4+PC9tc3VwPjwvbXJvdz48L21mcmFjPjwvbWF0aD5vI5eYAAAAAElFTkSuQmCC" class="Wirisformula" alt="fraction numerator d y over denominator d x end fraction equals fraction numerator x y over denominator x to the power of 2 end exponent plus y to the power of 2 end exponent end fraction" width="107" height="41" style="vertical-align:-18px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mfrac»«mrow»«mi»d«/mi»«mi»y«/mi»«/mrow»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mi»x«/mi»«mi»y«/mi»«/mrow»«mrow»«msup»«mrow»«mi»x«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«mo»+«/mo»«msup»«mrow»«mi»y«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«/mrow»«/mfrac»«/math»'/> is

Solution for the question - the solution of the differential equation (dy)/(dx)=(xy)/(x^(2)+y^(2)) is y=e^(x^(2))+y^(2)+c '/>   y=e^(x^(2))+e^(y^(2)+c) '/>

The solution of the differential equation (dy)/(dx)=(xy)/(x^(2)-Turito

It is a homogenous equation, solve it by putting <img src="data:image/png;base64,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" class="Wirisformula" alt="y equals v x" width="45" height="12" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»y«/mi»«mo»=«/mo»«mi»v«/mi»«mi»x«/mi»«/math»'/>and <img src="data:image/png;base64,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" class="Wirisformula" alt="fraction numerator d y over denominator d x end fraction equals v plus x fraction numerator d v over denominator d x end fraction" width="112" height="35" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mfrac»«mrow»«mi»d«/mi»«mi»y«/mi»«/mrow»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mi»v«/mi»«mo»+«/mo»«mi»x«/mi»«mfrac»«mrow»«mi»d«/mi»«mi»v«/mi»«/mrow»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«/math»'/>.

The solution of the differential equation <img src="data:image/png;base64,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" class="Wirisformula" alt="x d y minus y d x equals left parenthesis square root of x to the power of 2 end exponent plus y to the power of 2 end exponent right parenthesis end root d x" width="192" height="24" style="vertical-align:-4px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»x«/mi»«mi»d«/mi»«mi»y«/mi»«mo»-«/mo»«mi»y«/mi»«mi»d«/mi»«mi»x«/mi»«mo»=«/mo»«mo»(«/mo»«msqrt»«msup»«mrow»«mi»x«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«mo»+«/mo»«msup»«mrow»«mi»y«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«mo»)«/mo»«/msqrt»«mi»d«/mi»«mi»x«/mi»«/math»'/> is

Solution for the question - the solution of the differential equation xdy-ydx=(sqrt(x^(2)+y^(2)))dxis none of thesey+sqrt(x^(2)+y^(2))+cx^(2)=0 '/>

The solution of the differential equation xdy-ydx=(sqrt(x^(2)+y-Turito

The solution of the equation <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFsAAAAmCAYAAACriueGAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAAlVJREFUeNrtmj9Iw0AUxoODiIiLiEM3cRQRHEQcRHAQkRJcxEGkCM5uTtJBBHHIIK5FRKQg4iDiIiLi4CIiIg5CJ3EVpyIu9Tt4hXBcaf683LW9++AHycXU914u7y7weV5yVUGX55S5RsCrK4Me+aDcwfnVTP3jPnAAfsAvOAeHYIuul8Cy4r5NsGsg3nWwpxjfoWucxWbNXfTkO1Cg435QpGB8+ps1sC/d1ws+wIChCfIMhkLnBZog3DObNfft0AwOS/xYjo4XwJl0vUj3mtI8COh4Dtxm1EZYc/+kNiLP9mroXDzBt9D5IKiAHsN99wbMgJcIs6wWAZXYch8H94rxSWot8jawroB6lmmJGP7AWMYLJEvuS+BEMb4CjqSxBzBMVFpg/z1NC3lA8WZZbJbcfUU/8ugBbEhjxyAPTsGq4UKLpC9poRIt8CnBYhWn2Cy5i2DfqZ0ITYAr8EULg/zKllrgQ0f0zGupuIsN3lCuYrPlLrZPF7S/fgSz4FuxAPgUYN5gobsp1pziWpl2KFl94GnNPU8Pw0Zpz128ulOWFltr7qPUy21UW+ae9KPCyYlndqWlXeNuxbxdG3FycnJyslvOxqBJzsagUZ1uYzCmZjYGIQ7rAKd0xsNmZYhiY6grrXWAW7riYbMyRLEx1JXWOsAtXfGwWRmi2BjCimMd0KG2sTLEsTGE+1RS60AW0hVPaitDHBuDUFrrALd0xpPayhDHxsBhHeCU7nhSWxmi2hi4rANcMhEPi5WhmY3BlHWgkayxMtgsm20c2mWzjUOrYlkZ/gGNJQ6QQVQ1tAAAAP90RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWZyYWM+PG1yb3c+PG1pPmQ8L21pPjxtaT55PC9taT48L21yb3c+PG1yb3c+PG1pPmQ8L21pPjxtaT54PC9taT48L21yb3c+PC9tZnJhYz48bW8+PTwvbW8+PG1mcmFjPjxtcm93PjxtaT54PC9taT48bW8+KzwvbW8+PG1pPnk8L21pPjwvbXJvdz48bXJvdz48bWk+eDwvbWk+PG1vPi08L21vPjxtaT55PC9taT48L21yb3c+PC9tZnJhYz48L21hdGg+hllqoQAAAABJRU5ErkJggg==" class="Wirisformula" alt="fraction numerator d y over denominator d x end fraction equals fraction numerator x plus y over denominator x minus y end fraction" width="91" height="38" style="vertical-align:-15px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mfrac»«mrow»«mi»d«/mi»«mi»y«/mi»«/mrow»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mi»x«/mi»«mo»+«/mo»«mi»y«/mi»«/mrow»«mrow»«mi»x«/mi»«mo»-«/mo»«mi»y«/mi»«/mrow»«/mfrac»«/math»'/> is

Solution for the question - the solution of the equation (dy)/(dx)=(x+y)/(x-y) is none of thesec(x^(2)-y^(2))=e^(tan^(-1))(y//x) '/>

The solution of the equation (dy)/(dx)=(x+y)/(x-y) is -Turito

Given equation is <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAANYAAAAuCAYAAABUIudaAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAABR5JREFUeNrtnX9kVlEYx4+ZTGak0pI0M7M/kkj6yaTMzMxEpj/SpmSS9Efsj8pKUoqVZGQlScYkqcnIrMkkJa/1U/RXUu8/ayqVtazn8T7X7q6zds56z8459zxfvrzvve993/Oezz3nPve5594jRHr0A1wgWMzEQy0AXwVnwWPgW45UXAV4mJkwE1/VB/4ALgcfBH8E1ztQrkZwNzNhJj4KYU2Ad4OX0+sh8MI5Lkcx+CJ4FPyLeuhL4DZaj713k2S7Q+BTzMQKE9Qe8BnJtidpXbAaolCjkN7bCDfwNwfALfS6BNxOO1QjfQZ3srOJ7eaD31nY4ZjJVD0HL4m9b6EGGKxKqKIGLJfjWKIXjISNZhm9rgP3JNa307bMxA6TSLXgDnq9DdwfehjYSBC7LJfjA4UdyR7zR+w9HpVext4vBr8HFzETa0ziegCuBmdSGEFo6wRBbLFYhtXgQcnydZJeOw61g86vmIldJvFzXQxfV3HaIhdaTQi72abt4BuS5TvB1xLLHolclqycjlYFzMQ6E9QmSmx00GeCV4YgVlkOfXokyxHsvsSy6+AG8E3wLmbiBBPs5O6KXCIJQ8dnHArmUqjjlnt+BPKawg/UGnCvyF23qZOEG5h2H2YmTjDB89z7iYZUP83RLhgVU8846kBZMFV7m3aqx+At4BFJYiI6sW9gJtaZzKP1yyTb4gXkWk8ZYFa2E/yEfJmWKauGIPZ59KcbCHJa5SOTtKk/0XHXC83LBzsIok/DUzDs2OBo2Sby8B0+MkmTsP4vSpZfEBpJmVaC2OnJn15Jcb5IccPyjUnadIuihqS20DoldYnJ8WgsNxoWM8kfi5ks0widOyaFy7KqP94t5OO+WPYaFjOxq/F/rBvTOV9BiNvy0PrT7Hz3iszEPBsTDeuX6peMUuFKuKNy5ojFTOyGgtlpQsEi1VCwgFrnODNwpmExEzeSF7LrbzWqyYuFtCNkuS6daVjMxL62C/ldBTg+UindXksQ73JdOtOwmIkbwtH7OHSukMLCI0I+0l+qJoJ43UDBivjEeFZiJm6wiR7ig8kKvE0JhzQVq24c3fNz2EDBsOd9yh2ftphJCmTyesl58GmuYmYSahyJEFcY+O434PVcxcwkRGH8+N3A95aBv4jJpwu5nGhA49V0fCJSBTNhNv+rSmFuBPUB4dfIbLx2tF/kHt/FTJiNtnB0bnWsok3dLHgP3OzpEZyZMBstHSNovdQL4CPEMgZ+B0ONb+BSz8Dhzj3ITJiNrvBRv3iLMT585Q74qzDziCqVlG4l7VQZR+pmKcXx5czEGSa22Wj1WggSh2W0GSzoOfqdfyl6ys+EA/VSSUeMpczEGSYusHFOmNLdrPhZ2xARGN6iUcJMnGESGhsllQm9lK5JiCqzkiC4KmYypw1LdVaSENhItUiyDJ/VoJPSNQlRZVYSF8YGhsQkksqsJGljM6Mq6JwA/+jaxDrdlK7JygplVhKfmETiWUkkOkoQP4upz70ropCjNM8QZzvKOZRZSXxiEhfPSjKN8FzlZ2xHxZ7nheZ3mO4dQ5iVxDcm8bLyrCTT6Dd4L73GlO5xxyCGMCuJb0xQPCvJDHoIfkWvZzNy2jTEEGYl8Y0Jz0qioK3gP+CN4E9Cf+S0aYghzEriExOelURDeHL8VuindOcilZr2WUl8YpLWWUmM6QpBaHawbGmflcRHJixFLSGIixwsm8uzkoTKhKWhVgfL5PqsJCEyYWmqkKuAmYSkv36+wp5Szl9RAAABZ3RFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtbz4mI3gyMjJCOzwvbW8+PG1mcmFjPjxtcm93PjxtaT5kPC9taT48bWk+eTwvbWk+PC9tcm93Pjxtc3FydD48bW4+MTwvbW4+PG1vPi08L21vPjxtc3VwPjxtaT55PC9taT48bW4+MjwvbW4+PC9tc3VwPjwvbXNxcnQ+PC9tZnJhYz48bW8+KzwvbW8+PG1vPiYjeDIyMkI7PC9tbz48bWZyYWM+PG1yb3c+PG1pPmQ8L21pPjxtaT54PC9taT48L21yb3c+PG1zcXJ0Pjxtbj4xPC9tbj48bW8+LTwvbW8+PG1zdXA+PG1pPng8L21pPjxtbj4yPC9tbj48L21zdXA+PC9tc3FydD48L21mcmFjPjxtbz49PC9tbz48bW4+MDwvbW4+PC9tYXRoPiNhCb0AAAAASUVORK5CYII=" class="Wirisformula" alt="not stretchy integral fraction numerator d y over denominator square root of 1 minus y to the power of 2 end exponent end root end fraction plus not stretchy integral fraction numerator d x over denominator square root of 1 minus x to the power of 2 end exponent end root end fraction equals 0" width="214" height="46" style="vertical-align:-23px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mrow»«mo stretchy=¨false¨»∫«/mo»«mrow»«mfrac»«mrow»«mi»d«/mi»«mi»y«/mi»«/mrow»«mrow»«msqrt»«mn»1«/mn»«mo»-«/mo»«msup»«mrow»«mi»y«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«/msqrt»«/mrow»«/mfrac»«mo»+«/mo»«mrow»«mo stretchy=¨false¨»∫«/mo»«mrow»«mfrac»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«mrow»«msqrt»«mn»1«/mn»«mo»-«/mo»«msup»«mrow»«mi»x«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«/msqrt»«/mrow»«/mfrac»«mo»=«/mo»«mn»0«/mn»«/mrow»«/mrow»«/mrow»«/mrow»«/math»'/> Integrating we get, <img src="data:image/png;base64,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" class="Wirisformula" alt="sin to the power of negative 1 end exponent invisible function application y plus sin to the power of negative 1 end exponent invisible function application x equals c" width="147" height="19" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mrow»«mrow»«msup»«mrow»«mi»sin«/mi»«/mrow»«mrow»«mo»-«/mo»«mn»1«/mn»«/mrow»«/msup»«/mrow»«mo»⁡«/mo»«mrow»«mi»y«/mi»«/mrow»«/mrow»«mo»+«/mo»«mrow»«mrow»«msup»«mrow»«mi»sin«/mi»«/mrow»«mrow»«mo»-«/mo»«mn»1«/mn»«/mrow»«/msup»«/mrow»«mo»⁡«/mo»«mrow»«mi»x«/mi»«/mrow»«/mrow»«mo»=«/mo»«mi»c«/mi»«/math»'/>.

The solution of <img src="data:image/png;base64,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" class="Wirisformula" alt="fraction numerator d y over denominator d x end fraction plus square root of open parentheses fraction numerator 1 minus y to the power of 2 end exponent over denominator 1 minus x to the power of 2 end exponent end fraction close parentheses end root equals 0" width="157" height="51" style="vertical-align:-20px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mfrac»«mrow»«mi»d«/mi»«mi»y«/mi»«/mrow»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mo»+«/mo»«msqrt»«mfenced separators=¨|¨»«mrow»«mfrac»«mrow»«mn»1«/mn»«mo»-«/mo»«msup»«mrow»«mi»y«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«/mrow»«mrow»«mn»1«/mn»«mo»-«/mo»«msup»«mrow»«mi»x«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«/mrow»«/mfrac»«/mrow»«/mfenced»«/msqrt»«mo»=«/mo»«mn»0«/mn»«/math»'/> is

Solution for the question - the solution of (dy)/(dx)+sqrt(((1-y^(2))/(1-x^(2))))=0 is none of thesesec^(-1)x+cosec^(-1)x=c '/>

The solution of (dy)/(dx)+sqrt(((1-y^(2))/(1-x^(2))))=0 is -Turito

Given equation can be written as <img src="data:image/png;base64,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" class="Wirisformula" alt="open parentheses fraction numerator 1 minus x to the power of 2 end exponent over denominator x end fraction close parentheses d x equals fraction numerator d y over denominator y end fraction" width="133" height="44" style="vertical-align:-15px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mfenced separators=¨|¨»«mrow»«mfrac»«mrow»«mn»1«/mn»«mo»-«/mo»«msup»«mrow»«mi»x«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«/mrow»«mrow»«mi»x«/mi»«/mrow»«/mfrac»«/mrow»«/mfenced»«mi»d«/mi»«mi»x«/mi»«mo»=«/mo»«mfrac»«mrow»«mi»d«/mi»«mi»y«/mi»«/mrow»«mrow»«mi»y«/mi»«/mrow»«/mfrac»«/math»'/> After integration, we get <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALYAAAAnCAYAAACiyrLiAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAbSkFbcgAAA15JREFUeNrtnT9oFFEQxh9HkCBHIEiQICIcIkFCGglyHGIjIkHERkREJAgWVlfYioUIYpFC7ERERAQJIYQjCGIRjiABkSBBgmBpZXdFkCCcM+x3sKxvz73L/smO3w8+cm+zt+ybmbf73sxm4xzx0YV2Reui4zQJsURFdEf0maYgFvlFExBrnBWt0QzEEpOYY9doCmKFE6IWgpsQM1fqVdEYTUHKwC3RI8/2B/hdDw3qKZqLlAlN3R0OtedFTyP7dD0iZF9zQbSAz+dEH2gSYoX3LkjjbYoO0RzECk0XlMtnaApihYZoEdORazQHsYAWWlZEB0VV0SdORUjZmXBBGi8cyBdFr2ga21hOaR0QLYmOeH73xgWZEvrAaF+Yq6UPGNjkv/RB10pg6xz0qwtSY/rzUsx361iI6XPL311QzfMdL2lJm4GdjQ+ei656vqvpz4c5BHba8eSQBHgs+oHj6pRzvN+JnMZBp9GeRrse2W8K28+EMg+v+5xIkpJ22YPzX0oaDGn74CaCIIxmiL65ZNmhvQR2FvFURTzpoBzDWuouBlDsiSxGd0B7ObLthej2AEZgSTt5MKTtgznR28i2+6J7OUxFsognvfs/GfREOhgB0exCJ7LtZ/TSn8AIg5S093oFzEp5BHbaPlBbb4XaE7g6juZw90m7L5U++/b9YtxJ7ybcr1+nLZe00wyGLHywE/q8AF/ksXhMuy+zonaWV4sdjJ6kRmBJu1gftDFvreFqXckpsNPuyxwWikPNiaKr1sueg73zLADGY4zAknbxPniJY+qC7EYKWZui+nJKtD3MicxiRJ9EewbthmfktJHpqGBxuOH+fmUBS9rF+6A3DdS035cUzq/ovmwiIzKCrEjTc7zYvOM25kFbGGE+NAfdyyNuoBOdyC2nDCXt/RbYafogfJXsuvgccpn6ctQFr8b4jYGaeS1ER1sZ0ni9+X4HRtQrwHUjgyTOBxrQH430JXNWMKqUSbTnS2CwNSxgq2jrbXK9pIvapD5Y9cxhy9qXzLmCW0GvBNp05eXYkPPPokniA632tYz0hQwB39VHzFHHdIQQM4xiFd6gKYgVtAigD+ScpymIFWoIav7nAmIGff73mQvK/ISYQBP/+nzyCE1BLNFyfKsqMUjef0hAcuIPuD9sXAnHa3UAAAEMdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1pPmxvZzwvbWk+PG1vPiYjeDIwNjE7PC9tbz48bWk+eDwvbWk+PG1vPi08L21vPjxtZnJhYz48bXN1cD48bWk+eDwvbWk+PG1uPjI8L21uPjwvbXN1cD48bW4+MjwvbW4+PC9tZnJhYz48bW8+PTwvbW8+PG1pPmxvZzwvbWk+PG1vPiYjeDIwNjE7PC9tbz48bWk+eTwvbWk+PG1vPis8L21vPjxtaT5sb2c8L21pPjxtbz4mI3gyMDYxOzwvbW8+PG1pPmM8L21pPjwvbWF0aD7igSOJAAAAAElFTkSuQmCC" class="Wirisformula" alt="log invisible function application x minus fraction numerator x to the power of 2 end exponent over denominator 2 end fraction equals log invisible function application y plus log invisible function application c" width="182" height="39" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mrow»«mrow»«mi»log«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mi»x«/mi»«/mrow»«/mrow»«mo»-«/mo»«mfrac»«mrow»«msup»«mrow»«mi»x«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/mfrac»«mo»=«/mo»«mrow»«mrow»«mi»log«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mi»y«/mi»«/mrow»«/mrow»«mo»+«/mo»«mrow»«mrow»«mi»log«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mi»c«/mi»«/mrow»«/mrow»«/math»'/> Þ <img src="data:image/png;base64,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" class="Wirisformula" alt="log invisible function application x to the power of 2 end exponent minus log invisible function application y to the power of 2 end exponent plus log invisible function application c equals x to the power of 2 end exponent" width="190" height="19" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mrow»«mrow»«mi»log«/mi»«/mrow»«mo»⁡«/mo»«mrow»«msup»«mrow»«mi»x«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«/mrow»«/mrow»«mo»-«/mo»«mrow»«mrow»«mi»log«/mi»«/mrow»«mo»⁡«/mo»«mrow»«msup»«mrow»«mi»y«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«/mrow»«/mrow»«mo»+«/mo»«mrow»«mrow»«mi»log«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mi»c«/mi»«/mrow»«/mrow»«mo»=«/mo»«msup»«mrow»«mi»x«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«/math»'/>Þ<img src="data:image/png;base64,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" class="Wirisformula" alt="log invisible function application fraction numerator c x to the power of 2 end exponent over denominator y to the power of 2 end exponent end fraction equals x to the power of 2 end exponent" width="96" height="45" style="vertical-align:-18px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mrow»«mrow»«mi»log«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mfrac»«mrow»«mi»c«/mi»«msup»«mrow»«mi»x«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«/mrow»«mrow»«msup»«mrow»«mi»y«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«/mrow»«/mfrac»«/mrow»«/mrow»«mo»=«/mo»«msup»«mrow»«mi»x«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«/math»'/> Þ <img src="data:image/png;base64,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" class="Wirisformula" alt="fraction numerator c x to the power of 2 end exponent over denominator y to the power of 2 end exponent end fraction equals e to the power of x end exponent to the power of 2 end exponent" width="78" height="45" style="vertical-align:-18px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mfrac»«mrow»«mi»c«/mi»«msup»«mrow»«mi»x«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«/mrow»«mrow»«msup»«mrow»«mi»y«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«/mrow»«/mfrac»«mo»=«/mo»«msup»«mrow»«msup»«mrow»«mi»e«/mi»«/mrow»«mrow»«mi»x«/mi»«/mrow»«/msup»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«/math»'/>Þ<img src="data:image/png;base64,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" class="Wirisformula" alt="c x to the power of 2 end exponent equals y to the power of 2 end exponent e to the power of x to the power of 2 end exponent end exponent" width="85" height="22" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»c«/mi»«msup»«mrow»«mi»x«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«mo»=«/mo»«msup»«mrow»«mi»y«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«msup»«mrow»«mi»e«/mi»«/mrow»«mrow»«msup»«mrow»«mi»x«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«/mrow»«/msup»«/math»'/>.

Solution of <img src="data:image/png;base64,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" class="Wirisformula" alt="y d x minus x d y equals x to the power of 2 end exponent y d x" width="140" height="19" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»y«/mi»«mi»d«/mi»«mi»x«/mi»«mo»-«/mo»«mi»x«/mi»«mi»d«/mi»«mi»y«/mi»«mo»=«/mo»«msup»«mrow»«mi»x«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«mi»y«/mi»«mi»d«/mi»«mi»x«/mi»«/math»'/> is

Solution for the question - solution of ydx-xdy=x^(2)ydx is y^(2)e^(-x^(2))=cx^(2) '/>   y^(2)e^(x^(2))=cx^(2) '/>  ye^(-x^(2))=cx^(2) '/>   ye^(x^(2))=cx^(2) '/>

Solution of ydx-xdy=x^(2)ydx is -Turito

<img src="data:image/png;base64,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" class="Wirisformula" alt="not stretchy integral fraction numerator d y over denominator y end fraction equals not stretchy integral 2 x d x" width="117" height="38" style="vertical-align:-15px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mrow»«mo stretchy=¨false¨»∫«/mo»«mrow»«mfrac»«mrow»«mi»d«/mi»«mi»y«/mi»«/mrow»«mrow»«mi»y«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mrow»«mo stretchy=¨false¨»∫«/mo»«mrow»«mn»2«/mn»«mi»x«/mi»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mrow»«/mrow»«/mrow»«/math»'/>Þ<img src="data:image/png;base64,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" class="Wirisformula" alt="log subscript e end subscript invisible function application y equals x to the power of 2 end exponent plus c" width="104" height="21" style="vertical-align:-5px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mrow»«mrow»«msub»«mrow»«mi»log«/mi»«/mrow»«mrow»«mi»e«/mi»«/mrow»«/msub»«/mrow»«mo»⁡«/mo»«mrow»«mi»y«/mi»«/mrow»«/mrow»«mo»=«/mo»«msup»«mrow»«mi»x«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«mo»+«/mo»«mi»c«/mi»«/math»'/> Þ <img src="data:image/png;base64,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" class="Wirisformula" alt="y equals e to the power of x to the power of 2 end exponent plus c end exponent equals e to the power of c end exponent e to the power of x to the power of 2 end exponent end exponent" width="128" height="22" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»y«/mi»«mo»=«/mo»«msup»«mrow»«mi»e«/mi»«/mrow»«mrow»«msup»«mrow»«mi»x«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«mo»+«/mo»«mi»c«/mi»«/mrow»«/msup»«mo»=«/mo»«msup»«mrow»«mi»e«/mi»«/mrow»«mrow»«mi»c«/mi»«/mrow»«/msup»«msup»«mrow»«mi»e«/mi»«/mrow»«mrow»«msup»«mrow»«mi»x«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«/mrow»«/msup»«/math»'/>Þ<img src="data:image/png;base64,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" class="Wirisformula" alt="y equals c e to the power of x to the power of 2 end exponent end exponent" width="58" height="22" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»y«/mi»«mo»=«/mo»«mi»c«/mi»«msup»«mrow»«mi»e«/mi»«/mrow»«mrow»«msup»«mrow»«mi»x«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«/mrow»«/msup»«/math»'/>.

Solution of differential equation <img src="data:image/png;base64,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" class="Wirisformula" alt="fraction numerator d y over denominator d x end fraction equals 2 x y" width="75" height="35" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mfrac»«mrow»«mi»d«/mi»«mi»y«/mi»«/mrow»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mn»2«/mn»«mi»x«/mi»«mi»y«/mi»«/math»'/> is

Solution for the question - solution of differential equation (dy)/(dx)=2xy is y=x^(2)+c '/>   y=e^(-x^(2))+c '/>   y^(2)=2x^(2)+c '/>  y=ce^(x^(2)) '/>

Solution of differential equation (dy)/(dx)=2xy is -Turito

<img src="data:image/png;base64,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" class="Wirisformula" alt="x left parenthesis e to the power of 2 y end exponent minus 1 right parenthesis d y plus left parenthesis x to the power of 2 end exponent minus 1 right parenthesis e to the power of y end exponent d x equals 0" width="230" height="19" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»x«/mi»«mo»(«/mo»«msup»«mrow»«mi»e«/mi»«/mrow»«mrow»«mn»2«/mn»«mi»y«/mi»«/mrow»«/msup»«mo»-«/mo»«mn»1«/mn»«mo»)«/mo»«mi»d«/mi»«mi»y«/mi»«mo»+«/mo»«mo»(«/mo»«msup»«mrow»«mi»x«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«mo»-«/mo»«mn»1«/mn»«mo»)«/mo»«msup»«mrow»«mi»e«/mi»«/mrow»«mrow»«mi»y«/mi»«/mrow»«/msup»«mi»d«/mi»«mi»x«/mi»«mo»=«/mo»«mn»0«/mn»«/math»'/> Þ <img src="data:image/png;base64,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" class="Wirisformula" alt="not stretchy integral fraction numerator e to the power of 2 y end exponent minus 1 over denominator e to the power of y end exponent end fraction d y equals not stretchy integral fraction numerator 1 minus x to the power of 2 end exponent over denominator x end fraction d x" width="203" height="42" style="vertical-align:-15px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mrow»«mo stretchy=¨false¨»∫«/mo»«mrow»«mfrac»«mrow»«msup»«mrow»«mi»e«/mi»«/mrow»«mrow»«mn»2«/mn»«mi»y«/mi»«/mrow»«/msup»«mo»-«/mo»«mn»1«/mn»«/mrow»«mrow»«msup»«mrow»«mi»e«/mi»«/mrow»«mrow»«mi»y«/mi»«/mrow»«/msup»«/mrow»«/mfrac»«/mrow»«/mrow»«mi»d«/mi»«mi»y«/mi»«mo»=«/mo»«mrow»«mo stretchy=¨false¨»∫«/mo»«mrow»«mfrac»«mrow»«mn»1«/mn»«mo»-«/mo»«msup»«mrow»«mi»x«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«/mrow»«mrow»«mi»x«/mi»«/mrow»«/mfrac»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mrow»«/math»'/>Þ <img src="data:image/png;base64,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" class="Wirisformula" alt="e to the power of y end exponent plus e to the power of negative y end exponent equals log invisible function application x minus fraction numerator x to the power of 2 end exponent over denominator 2 end fraction plus c" width="185" height="39" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«msup»«mrow»«mi»e«/mi»«/mrow»«mrow»«mi»y«/mi»«/mrow»«/msup»«mo»+«/mo»«msup»«mrow»«mi»e«/mi»«/mrow»«mrow»«mo»-«/mo»«mi»y«/mi»«/mrow»«/msup»«mo»=«/mo»«mrow»«mrow»«mi»log«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mi»x«/mi»«/mrow»«/mrow»«mo»-«/mo»«mfrac»«mrow»«msup»«mrow»«mi»x«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/mfrac»«mo»+«/mo»«mi»c«/mi»«/math»'/>.

The solution of the differential equation <img src="data:image/png;base64,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" class="Wirisformula" alt="x left parenthesis e to the power of 2 y end exponent minus 1 right parenthesis d y plus left parenthesis x to the power of 2 end exponent minus 1 right parenthesis e to the power of y end exponent d x equals 0" width="230" height="19" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»x«/mi»«mo»(«/mo»«msup»«mrow»«mi»e«/mi»«/mrow»«mrow»«mn»2«/mn»«mi»y«/mi»«/mrow»«/msup»«mo»-«/mo»«mn»1«/mn»«mo»)«/mo»«mi»d«/mi»«mi»y«/mi»«mo»+«/mo»«mo»(«/mo»«msup»«mrow»«mi»x«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«mo»-«/mo»«mn»1«/mn»«mo»)«/mo»«msup»«mrow»«mi»e«/mi»«/mrow»«mrow»«mi»y«/mi»«/mrow»«/msup»«mi»d«/mi»«mi»x«/mi»«mo»=«/mo»«mn»0«/mn»«/math»'/> is

Solution for the question - the solution of the differential equation x(e^(2y)-1)dy+(x^(2)-1)e^(y)dx=0is none of thesee^(y)+e^(-y)=log x+(x^(2))/(2)+c '/>

The solution of the differential equation x(e^(2y)-1)dy+(x^(2)--Turito

Here <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAHQAAAAjCAYAAABFES5oAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAAyVJREFUeNrtmk+EVVEcx69ZjGRExkhGYqRV8phFkmRokeQZMTKLZAwjGWmXFplFYrRokdllJCPDGC2SRJKMMZskSYuYVdomLZ7xPF7fH9/LcTr33XPvPfe+8+6cD1/ePe/eO/f9fnP+/L73RFF+WtBQFKgFJ6CvIQz1YRpaD2EYTEagJ9AfaA/ahFagu/x+FbpmuO4O9DCEzy9kjvwAzfHzIWgJ6rKXCjegR9p1B6Ef0GgIoV/cV3qiiiRrnJ8vQxva90u8NuAZPznk6r22pRxLL/ymHI9Bu9CBED6/aEAfDe1nOAzrJUzMY86fAc+4Cq0Z2mehZ1rbFjRB7Yb61N/SZMPQLkle0NqeQ03oBXS9ZnG4BS17+mzLfD4rZKX6nUOvMAm9hn5xIaSXKKs1NBtOQzueP+M2n9OKI9BL1p/yw6ag34YFzzRLmaaHP7hbMFgNzxM6ySnPKU2P/5PzJrTBhA4CW0ysM95AZ2s23IpZsujhqGHitst5/hTn1n4wwRKqxSB1LYIXH89wRb7H8uyYdt5b6LzhfvMJwXvA71wm1NZWlc703rdhMU0mPlnM26aEzrAHHmfbnKHm/gsNJ9zzM9cXkXL9Sgk91NZWHebzDjzSMw/nSOiU1iZ1c1tr6/S45yUaKMLFHL3DNqFZbNV2nl5SVGXUyts0O7Ik1Oa8TsrffgddgL5E6S8h8sYmi63arsOQK4jX/JQ180mHCe015MbzWDtLDZhzUWRjq9ZmyFW5x7nNVUKlB55LOFfaNxng2ZITamOrercocsFQwrCTN6FJZYsE9hUXJyNcmI2WmFAbW3XRsHgaeOaj/98CFUmoyVgYY82tJvBKZH6J4SqhNraqc2Oh33Nvh4E+6jChwo4yR8o8JTbouOG8da58yyDNVnVi/e2XLZw+mPNptmomc97EftvCeTPq7+uzXraqzJsLLoaAsIWzGpzbqmlbOOPFSFFvM1BRGZC2hTOmqLcZqACbLZwxRb3NQAXYbOHUnRVbbzNQMVm2cKoFcF5vM1AyWbZwCkW9zUDJZNnC6cLbDJSM7RZOV95moALStnD2y9sM9OAfgh4IH3y3aC8AAAD2dEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1mcmFjPjxtcm93PjxtaT5kPC9taT48bWk+eTwvbWk+PC9tcm93Pjxtcm93PjxtaT5kPC9taT48bWk+eDwvbWk+PC9tcm93PjwvbWZyYWM+PG1vPj08L21vPjxtcm93PjxtaT5zaW48L21pPjxtbz4mI3gyMDYxOzwvbW8+PG1vPig8L21vPjwvbXJvdz48bWk+eDwvbWk+PG1vPis8L21vPjxtaT55PC9taT48bW8+KTwvbW8+PC9tYXRoPu2oGigAAAAASUVORK5CYII=" class="Wirisformula" alt="fraction numerator d y over denominator d x end fraction equals sin invisible function application left parenthesis x plus y right parenthesis" width="116" height="35" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mfrac»«mrow»«mi»d«/mi»«mi»y«/mi»«/mrow»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mrow»«mrow»«mi»sin«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mo»(«/mo»«/mrow»«/mrow»«mi»x«/mi»«mo»+«/mo»«mi»y«/mi»«mo»)«/mo»«/math»'/> Now put <img src="data:image/png;base64,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" class="Wirisformula" alt="log invisible function application left parenthesis 1 plus y right parenthesis equals x plus fraction numerator x to the power of 2 end exponent over denominator 2 end fraction plus log invisible function application c" width="194" height="39" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mrow»«mrow»«mi»log«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mo»(«/mo»«/mrow»«/mrow»«mn»1«/mn»«mo»+«/mo»«mi»y«/mi»«mo»)«/mo»«mo»=«/mo»«mi»x«/mi»«mo»+«/mo»«mfrac»«mrow»«msup»«mrow»«mi»x«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/mfrac»«mo»+«/mo»«mrow»«mrow»«mi»log«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mi»c«/mi»«/mrow»«/mrow»«/math»'/>and <img src="data:image/png;base64,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" class="Wirisformula" alt="fraction numerator d y over denominator d x end fraction equals fraction numerator d v over denominator d x end fraction minus 1" width="102" height="35" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mfrac»«mrow»«mi»d«/mi»«mi»y«/mi»«/mrow»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mi»d«/mi»«mi»v«/mi»«/mrow»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mo»-«/mo»«mn»1«/mn»«/math»'/> Therefore <img src="data:image/png;base64,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" class="Wirisformula" alt="fraction numerator d y over denominator d x end fraction equals sin invisible function application left parenthesis x plus y right parenthesis" width="116" height="35" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mfrac»«mrow»«mi»d«/mi»«mi»y«/mi»«/mrow»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mrow»«mrow»«mi»sin«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mo»(«/mo»«/mrow»«/mrow»«mi»x«/mi»«mo»+«/mo»«mi»y«/mi»«mo»)«/mo»«/math»'/> reduces to <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGkAAAAjCAYAAACXQSQwAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAAnBJREFUeNrtmk1ERFEUx59ZJCORJBmJkVkl0SJpMYYWSZJo0XIMLVq1S4u0aJMWs0i7FkkyJC2SNhlpkUQykhbRKm3T6hmJ1znmPD3PffPufNzrzdzz48/rvg85Z+595/zftaxoYINiFhNZhkHPHIZoswAqcBiiQxdoD/QNKoPOQPugdTq/CDoR3FcEzXL41IPvnBtQlo67QVsgh2aTu/SVfPelQQ8cPj1semaMlzdQokoRcQ+a5vDp4YOWO//ssn1jmJRROp4B3XLo9DAWEOwJWgK9HIGW6BiXvkkOnx6wIDgWjC+DDn1jq6Bdek9dc+j0ltmngnFM3IpvDKu4c9ALzUBGE3HQqyfo46BL0KegtI5TeX7BYdNPP82QMhUHGdAXqFNwLfZRI20cC7bBIg7bYC3yfmYbLEKE2WBIDrQjuHebzjEhOBIKQsYGc3mid7ZLlpLJKEbWBkPQWcnTMVpgxUZ+Ne0qFcjaYC7YuKfJZenl37j65a4WG8xlDfRj/fuWjGJqscGQKSoq8nQNo6nMlrXBkuSuxGl5fOTlTg+yNlgf6MqXlLmAWcgoIMwG66DzCcG9Bar4pEhRKVmKwAucCcBdQx1OUmuUohxYg5OUpN7BrtJ7OAF/42f2d1r3sS8ZFJTCxmwRU5kkLDnna3yWQwnCz+xDNJYVNJBGbRFTmSScQT11JCnjG4tRxy56vhFbxBzJa+qxULDxuwvptB3J/0c0bswWMdWFA3baB9QAppqcJGO2iOmq7jasyreVZibJmC1iupIU9F5pJEnGbBHTlaScJbbyG0lS228R0/GBzH3ur1UxGweanCSkpbeI/QGwKQqSSYvW6QAAANV0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWZyYWM+PG1yb3c+PG1pPmQ8L21pPjxtaT52PC9taT48L21yb3c+PG1yb3c+PG1uPjE8L21uPjxtbz4rPC9tbz48bWk+c2luPC9taT48bW8+JiN4MjA2MTs8L21vPjxtaT52PC9taT48L21yb3c+PC9tZnJhYz48bW8+PTwvbW8+PG1pPmQ8L21pPjxtaT54PC9taT48L21hdGg+K3BsyQAAAABJRU5ErkJggg==" class="Wirisformula" alt="fraction numerator d v over denominator 1 plus sin invisible function application v end fraction equals d x" width="105" height="35" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mfrac»«mrow»«mi»d«/mi»«mi»v«/mi»«/mrow»«mrow»«mn»1«/mn»«mo»+«/mo»«mrow»«mrow»«mi»sin«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mi»v«/mi»«/mrow»«/mrow»«/mrow»«/mfrac»«mo»=«/mo»«mi»d«/mi»«mi»x«/mi»«/math»'/> Now on integrating both the sides, we get <img src="data:image/png;base64,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" class="Wirisformula" alt="tan invisible function application v minus sec invisible function application v equals x plus c" width="139" height="12" style="vertical-align:-1px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mrow»«mrow»«mi»tan«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mi»v«/mi»«/mrow»«/mrow»«mo»-«/mo»«mrow»«mrow»«mi»sec«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mi»v«/mi»«/mrow»«/mrow»«mo»=«/mo»«mi»x«/mi»«mo»+«/mo»«mi»c«/mi»«/math»'/> or <img src="data:image/png;base64,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" class="Wirisformula" alt="tan invisible function application left parenthesis x plus y right parenthesis minus sec invisible function application left parenthesis x plus y right parenthesis equals x plus c" width="215" height="17" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mrow»«mrow»«mi»tan«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mo»(«/mo»«/mrow»«/mrow»«mi»x«/mi»«mo»+«/mo»«mi»y«/mi»«mo»)«/mo»«mo»-«/mo»«mrow»«mrow»«mi»sec«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mo»(«/mo»«/mrow»«/mrow»«mi»x«/mi»«mo»+«/mo»«mi»y«/mi»«mo»)«/mo»«mo»=«/mo»«mi»x«/mi»«mo»+«/mo»«mi»c«/mi»«/math»'/>.

The solution of the equation <img src="data:image/png;base64,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" class="Wirisformula" alt="sin to the power of negative 1 end exponent invisible function application open parentheses fraction numerator d y over denominator d x end fraction close parentheses equals x plus y" width="139" height="38" style="vertical-align:-14px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mrow»«mrow»«msup»«mrow»«mi»sin«/mi»«/mrow»«mrow»«mo»-«/mo»«mn»1«/mn»«/mrow»«/msup»«/mrow»«mo»⁡«/mo»«mrow»«mfenced separators=¨|¨»«mrow»«mfrac»«mrow»«mi»d«/mi»«mi»y«/mi»«/mrow»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«/mrow»«/mfenced»«/mrow»«/mrow»«mo»=«/mo»«mi»x«/mi»«mo»+«/mo»«mi»y«/mi»«/math»'/> is

Solution for the question - the solution of the equation sin^(-1)((dy)/(dx))=x+y is none of thesetan(x+y)+sec(x+y)+x+c=0 '/>

The solution of the equation sin^(-1)((dy)/(dx))=x+y is -Turito

<img src="data:image/png;base64,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" class="Wirisformula" alt="fraction numerator d y over denominator d x end fraction equals fraction numerator left parenthesis 1 plus x right parenthesis y over denominator left parenthesis y minus 1 right parenthesis x end fraction" width="111" height="40" style="vertical-align:-15px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mfrac»«mrow»«mi»d«/mi»«mi»y«/mi»«/mrow»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mo»(«/mo»«mn»1«/mn»«mo»+«/mo»«mi»x«/mi»«mo»)«/mo»«mi»y«/mi»«/mrow»«mrow»«mo»(«/mo»«mi»y«/mi»«mo»-«/mo»«mn»1«/mn»«mo»)«/mo»«mi»x«/mi»«/mrow»«/mfrac»«/math»'/>can be written as <img src="data:image/png;base64,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" class="Wirisformula" alt="fraction numerator y minus 1 over denominator y end fraction d y equals fraction numerator left parenthesis 1 plus x right parenthesis over denominator x end fraction d x" width="157" height="40" style="vertical-align:-15px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mfrac»«mrow»«mi»y«/mi»«mo»-«/mo»«mn»1«/mn»«/mrow»«mrow»«mi»y«/mi»«/mrow»«/mfrac»«mi»d«/mi»«mi»y«/mi»«mo»=«/mo»«mfrac»«mrow»«mo»(«/mo»«mn»1«/mn»«mo»+«/mo»«mi»x«/mi»«mo»)«/mo»«/mrow»«mrow»«mi»x«/mi»«/mrow»«/mfrac»«mi»d«/mi»«mi»x«/mi»«/math»'/> Þ <img src="data:image/png;base64,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" class="Wirisformula" alt="open parentheses 1 minus fraction numerator 1 over denominator y end fraction close parentheses d y equals open parentheses 1 plus fraction numerator 1 over denominator x end fraction close parentheses d x" width="176" height="39" style="vertical-align:-15px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mfenced separators=¨|¨»«mrow»«mn»1«/mn»«mo»-«/mo»«mfrac»«mrow»«mn»1«/mn»«/mrow»«mrow»«mi»y«/mi»«/mrow»«/mfrac»«/mrow»«/mfenced»«mi»d«/mi»«mi»y«/mi»«mo»=«/mo»«mfenced separators=¨|¨»«mrow»«mn»1«/mn»«mo»+«/mo»«mfrac»«mrow»«mn»1«/mn»«/mrow»«mrow»«mi»x«/mi»«/mrow»«/mfrac»«/mrow»«/mfenced»«mi»d«/mi»«mi»x«/mi»«/math»'/> Þ <img src="data:image/png;base64,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" class="Wirisformula" alt="left parenthesis y minus log invisible function application y right parenthesis equals left parenthesis x plus log invisible function application x right parenthesis plus c" width="187" height="17" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mo»(«/mo»«mi»y«/mi»«mo»-«/mo»«mrow»«mrow»«mi»log«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mi»y«/mi»«/mrow»«/mrow»«mo»)«/mo»«mo»=«/mo»«mo»(«/mo»«mi»x«/mi»«mo»+«/mo»«mrow»«mrow»«mi»log«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mi»x«/mi»«/mrow»«/mrow»«mo»)«/mo»«mo»+«/mo»«mi»c«/mi»«/math»'/> Þ<img src="data:image/png;base64,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" class="Wirisformula" alt="x minus y plus log invisible function application x y equals c" width="124" height="15" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»x«/mi»«mo»-«/mo»«mi»y«/mi»«mo»+«/mo»«mrow»«mrow»«mi»log«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mi»x«/mi»«/mrow»«/mrow»«mi»y«/mi»«mo»=«/mo»«mi»c«/mi»«/math»'/>.

The solution of the differential equation <img src="data:image/png;base64,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" class="Wirisformula" alt="fraction numerator d y over denominator d x end fraction equals fraction numerator left parenthesis 1 plus x right parenthesis y over denominator left parenthesis y minus 1 right parenthesis x end fraction" width="111" height="40" style="vertical-align:-15px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mfrac»«mrow»«mi»d«/mi»«mi»y«/mi»«/mrow»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mo»(«/mo»«mn»1«/mn»«mo»+«/mo»«mi»x«/mi»«mo»)«/mo»«mi»y«/mi»«/mrow»«mrow»«mo»(«/mo»«mi»y«/mi»«mo»-«/mo»«mn»1«/mn»«mo»)«/mo»«mi»x«/mi»«/mrow»«/mfrac»«/math»'/> is

Solution for the question - the solution of the differential equation (dy)/(dx)=((1+x)y)/((y-1)x) is none of theselog xy+x-y=c '/>

The solution of the differential equation (dy)/(dx)=((1+x)y)/((-Turito

Here <img src="data:image/png;base64,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" class="Wirisformula" alt="fraction numerator d y over denominator d x end fraction equals fraction numerator 1 minus cos invisible function application x over denominator 1 plus cos invisible function application x end fraction equals tan to the power of 2 end exponent invisible function application fraction numerator x over denominator 2 end fraction" width="187" height="35" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mfrac»«mrow»«mi»d«/mi»«mi»y«/mi»«/mrow»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mn»1«/mn»«mo»-«/mo»«mrow»«mrow»«mi»cos«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mi»x«/mi»«/mrow»«/mrow»«/mrow»«mrow»«mn»1«/mn»«mo»+«/mo»«mrow»«mrow»«mi»cos«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mi»x«/mi»«/mrow»«/mrow»«/mrow»«/mfrac»«mo»=«/mo»«mrow»«mrow»«msup»«mrow»«mi»tan«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«/mrow»«mo»⁡«/mo»«mrow»«mfrac»«mrow»«mi»x«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/mfrac»«/mrow»«/mrow»«/math»'/> Þ <img src="data:image/png;base64,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" class="Wirisformula" alt="d y equals open parentheses sec to the power of 2 end exponent invisible function application fraction numerator x over denominator 2 end fraction minus 1 close parentheses d x" width="150" height="38" style="vertical-align:-14px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»d«/mi»«mi»y«/mi»«mo»=«/mo»«mfenced separators=¨|¨»«mrow»«mrow»«mrow»«msup»«mrow»«mi»sec«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«/mrow»«mo»⁡«/mo»«mrow»«mfrac»«mrow»«mi»x«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/mfrac»«/mrow»«/mrow»«mo»-«/mo»«mn»1«/mn»«/mrow»«/mfenced»«mi»d«/mi»«mi»x«/mi»«/math»'/> Now on integrating both the sides, we get <img src="data:image/png;base64,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" class="Wirisformula" alt="y equals 2 tan invisible function application fraction numerator x over denominator 2 end fraction minus x plus c" width="134" height="32" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»y«/mi»«mo»=«/mo»«mn»2«/mn»«mrow»«mrow»«mi»tan«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mfrac»«mrow»«mi»x«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/mfrac»«/mrow»«/mrow»«mo»-«/mo»«mi»x«/mi»«mo»+«/mo»«mi»c«/mi»«/math»'/>.

The solution of the differential equation <img src="data:image/png;base64,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" class="Wirisformula" alt="left parenthesis 1 plus cos invisible function application x right parenthesis d y equals left parenthesis 1 minus cos invisible function application x right parenthesis d x" width="205" height="17" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mo»(«/mo»«mn»1«/mn»«mo»+«/mo»«mrow»«mrow»«mi»cos«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mi»x«/mi»«/mrow»«/mrow»«mo»)«/mo»«mi»d«/mi»«mi»y«/mi»«mo»=«/mo»«mo»(«/mo»«mn»1«/mn»«mo»-«/mo»«mrow»«mrow»«mi»cos«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mi»x«/mi»«/mrow»«/mrow»«mo»)«/mo»«mi»d«/mi»«mi»x«/mi»«/math»'/> is

Solution for the question - the solution of the differential equation (1+cos x)dy=(1-cos x)dx is y=x-2tan (x)/(2)+c '/>   y=2tan (x)/(2)+x+c '/>   y=2tan x+x+c '/>

The solution of the differential equation (1+cos x)dy=(1-cos x)-Turito

<img src="data:image/png;base64,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" class="Wirisformula" alt="fraction numerator d y over denominator d x end fraction equals negative fraction numerator cos invisible function application x minus sin invisible function application x over denominator sin invisible function application x plus cos invisible function application x end fraction" width="159" height="35" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mfrac»«mrow»«mi»d«/mi»«mi»y«/mi»«/mrow»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mo»-«/mo»«mfrac»«mrow»«mrow»«mrow»«mi»cos«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mi»x«/mi»«/mrow»«/mrow»«mo»-«/mo»«mrow»«mrow»«mi»sin«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mi»x«/mi»«/mrow»«/mrow»«/mrow»«mrow»«mrow»«mrow»«mi»sin«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mi»x«/mi»«/mrow»«/mrow»«mo»+«/mo»«mrow»«mrow»«mi»cos«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mi»x«/mi»«/mrow»«/mrow»«/mrow»«/mfrac»«/math»'/> Þ <img src="data:image/png;base64,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" class="Wirisformula" alt="d y equals negative open parentheses fraction numerator cos invisible function application x minus sin invisible function application x over denominator sin invisible function application x plus cos invisible function application x end fraction close parentheses d x" width="184" height="38" style="vertical-align:-14px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»d«/mi»«mi»y«/mi»«mo»=«/mo»«mo»-«/mo»«mfenced separators=¨|¨»«mrow»«mfrac»«mrow»«mrow»«mrow»«mi»cos«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mi»x«/mi»«/mrow»«/mrow»«mo»-«/mo»«mrow»«mrow»«mi»sin«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mi»x«/mi»«/mrow»«/mrow»«/mrow»«mrow»«mrow»«mrow»«mi»sin«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mi»x«/mi»«/mrow»«/mrow»«mo»+«/mo»«mrow»«mrow»«mi»cos«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mi»x«/mi»«/mrow»«/mrow»«/mrow»«/mfrac»«/mrow»«/mfenced»«mi»d«/mi»«mi»x«/mi»«/math»'/> On integrating both sides, we get Þ <img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAANkAAAARCAYAAABQBQmvAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAOJ5y/mQAAA7pJREFUeNrtW0FoE0EUHYIEkSKUIkGKCD0UkRICIlJCEcGDFAlBCOJBJAhFpEgOXjyIBxGKhxzEWxERKYKUIkWKIFJKkFIoRUqRInjw4Cm3HoKEwPpH38qyzk5m0pkhm8yHRzO7k83Mm////P9ny5gXmdwlLHgarMsCuPYyZJInbHoanMlncO6lTyRwtOiFPhzXoMo5QiPF+uKNTFMKMDK/mG6lAWPzRjYERvaUMO95cS73NHLgIG28vCBcF1yvEZ6kRJmuEr4S2vhbSvjuNGGb8IvwnVAVPO8DYSZ2bYKwTmihf6AwrrBdwW/x39wgnBJ893aCgj3GPdPKVMRY+Jh+EG72wKcKJzrz4mvzyZGRmdSXUEbgoH/iuSuE0fDmLdyMyjHCN8JYwqC7waWRXQABU2hPoT0d63cG12ciSrIkeN4BIRu7ti1ZCJmRVcDtaVyrQrlFskPIRdq873MLHpuHw01CmZAhTIIHXT5VONGZVxbc2zYy0/oSGtgONqXjmMt9GPMfmSW8jX3pEeFhSsKi5ehkIp7qXezaS8KcwvM6gj6tqFfSMLJLsWsZeDmRXCHU8fmyhlfXVbxlhGay+yp8qnCiO6+2AyMzrS8Mu/Uz2SD4brUXaZ+ABR+1bCi97oYqO4/IKzYTlELFyMoohtzQNDJdBflIuEj4khBFmODwAN6WSe6r8KnCie682inUl4yk739eKZQ68jEbBmJjJwsUFyw4xCKEIcEiYvhJS0ZWw7jzBnjptV+gYQDdONGZl6tw0bS+nGeKxw8NxJwT2MUyKaqiqXqmVsK8AoHXLUp+/wHib9NGVkQoU1fcHXpVvKahnUyFE515uSp8mNaXWRQ5usorJLFLgkpTGnKykiCUWRFUDePJ7ajged1K+El51WGMjDu3VRScRlBUGLNkZIsKOZkKnyqc6MxrXlCAs5WTmdQXfra3rzIQvp3zUv4u638Rbdd89z2Ldh7tosDjNFDpyiAh32J/y7Px6pvsMJqXntcNGhnPgddiyscT8deWjIwrPi/bXwMP41h7XT67caI7L53D6KCP9IUh1+SVxSOIEmoivsoYTCmFRhYu3j686R7mk6QM4TnGFggXhUGbsfwhzDU7UJyThowsCw86Luj3BgtrQwqYfwcKUuqBTxknuvNy/VqVaX3hZ58b4GKXJZxtlthwvhCbS8gD/AvCbiUtLwjnmP7Ryj9ZE8Sfgyir8EYMnpe3qwl97zD/ry4uhOdhcwOgL1LhJ97vh2RBK9jOw9dkal7HvdjUl9+7voUbgi8svgAAASR0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+eTwvbWk+PG1vPj08L21vPjxtbz4tPC9tbz48bXJvdz48bWk+bG9nPC9taT48bW8+JiN4MjA2MTs8L21vPjxtbz4oPC9tbz48L21yb3c+PG1pPnNpbjwvbWk+PG1vPiYjeDIwNjE7PC9tbz48bWk+eDwvbWk+PG1vPis8L21vPjxtaT5jb3M8L21pPjxtbz4mI3gyMDYxOzwvbW8+PG1pPng8L21pPjxtbz4pPC9tbz48bW8+KzwvbW8+PG1pPmxvZzwvbWk+PG1vPiYjeDIwNjE7PC9tbz48bWk+YzwvbWk+PC9tYXRoPpAARY4AAAAASUVORK5CYII=" class="Wirisformula" alt="y equals negative log invisible function application left parenthesis sin invisible function application x plus cos invisible function application x right parenthesis plus log invisible function application c" width="217" height="17" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»y«/mi»«mo»=«/mo»«mo»-«/mo»«mrow»«mrow»«mi»log«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mo»(«/mo»«/mrow»«/mrow»«mrow»«mrow»«mi»sin«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mi»x«/mi»«/mrow»«/mrow»«mo»+«/mo»«mrow»«mrow»«mi»cos«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mi»x«/mi»«/mrow»«/mrow»«mo»)«/mo»«mo»+«/mo»«mrow»«mrow»«mi»log«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mi»c«/mi»«/mrow»«/mrow»«/math»'/> Þ <img src="data:image/png;base64,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" class="Wirisformula" alt="y equals log invisible function application open parentheses fraction numerator c over denominator sin invisible function application x plus cos invisible function application x end fraction close parentheses" width="161" height="38" style="vertical-align:-14px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»y«/mi»«mo»=«/mo»«mrow»«mrow»«mi»log«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mfenced separators=¨|¨»«mrow»«mfrac»«mrow»«mi»c«/mi»«/mrow»«mrow»«mrow»«mrow»«mi»sin«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mi»x«/mi»«/mrow»«/mrow»«mo»+«/mo»«mrow»«mrow»«mi»cos«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mi»x«/mi»«/mrow»«/mrow»«/mrow»«/mfrac»«/mrow»«/mfenced»«/mrow»«/mrow»«/math»'/> Þ <img src="data:image/png;base64,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" class="Wirisformula" alt="e to the power of y end exponent left parenthesis sin invisible function application x plus cos invisible function application x right parenthesis equals c" width="141" height="16" style="vertical-align:-2px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«msup»«mrow»«mi»e«/mi»«/mrow»«mrow»«mi»y«/mi»«/mrow»«/msup»«mo»(«/mo»«mrow»«mrow»«mi»sin«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mi»x«/mi»«/mrow»«/mrow»«mo»+«/mo»«mrow»«mrow»«mi»cos«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mi»x«/mi»«/mrow»«/mrow»«mo»)«/mo»«mo»=«/mo»«mi»c«/mi»«/math»'/>.

The solution of the differential equation <img src="data:image/png;base64,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" class="Wirisformula" alt="left parenthesis sin invisible function application x plus cos invisible function application x right parenthesis d y plus left parenthesis cos invisible function application x minus sin invisible function application x right parenthesis d x equals 0" width="280" height="17" style="vertical-align:-3px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mo»(«/mo»«mrow»«mrow»«mi»sin«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mi»x«/mi»«/mrow»«/mrow»«mo»+«/mo»«mrow»«mrow»«mi»cos«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mi»x«/mi»«/mrow»«/mrow»«mo»)«/mo»«mi»d«/mi»«mi»y«/mi»«mo»+«/mo»«mo»(«/mo»«mrow»«mrow»«mi»cos«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mi»x«/mi»«/mrow»«/mrow»«mo»-«/mo»«mrow»«mrow»«mi»sin«/mi»«/mrow»«mo»⁡«/mo»«mrow»«mi»x«/mi»«/mrow»«/mrow»«mo»)«/mo»«mi»d«/mi»«mi»x«/mi»«mo»=«/mo»«mn»0«/mn»«/math»'/> is

Solution for the question - the solution of the differential equation (sin x+cos x)dy+(cos x-sin x)dx=0is e^(x)(5sin x-cos x)=c '/>   e^(y)(cos x-sin x)=c '/>

The solution of the differential equation (sin x+cos x)dy+(cos -Turito

<img src="data:image/png;base64,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" class="Wirisformula" alt="left parenthesis 1 plus x to the power of 2 end exponent right parenthesis fraction numerator d y over denominator d x end fraction equals x" width="113" height="35" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mo»(«/mo»«mn»1«/mn»«mo»+«/mo»«msup»«mrow»«mi»x«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«mo»)«/mo»«mfrac»«mrow»«mi»d«/mi»«mi»y«/mi»«/mrow»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mi»x«/mi»«/math»'/> Þ <img src="data:image/png;base64,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" class="Wirisformula" alt="d y equals fraction numerator x over denominator 1 plus x to the power of 2 end exponent end fraction d x" width="111" height="35" style="vertical-align:-15px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»d«/mi»«mi»y«/mi»«mo»=«/mo»«mfrac»«mrow»«mi»x«/mi»«/mrow»«mrow»«mn»1«/mn»«mo»+«/mo»«msup»«mrow»«mi»x«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«/mrow»«/mfrac»«mi»d«/mi»«mi»x«/mi»«/math»'/> Þ <img src="data:image/png;base64,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" class="Wirisformula" alt="not stretchy integral d y equals not stretchy integral fraction numerator x over denominator 1 plus x to the power of 2 end exponent end fraction d x plus c" width="169" height="37" style="vertical-align:-15px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mrow»«mo stretchy=¨false¨»∫«/mo»«mrow»«mi»d«/mi»«mi»y«/mi»«/mrow»«/mrow»«mo»=«/mo»«mrow»«mo stretchy=¨false¨»∫«/mo»«mrow»«mfrac»«mrow»«mi»x«/mi»«/mrow»«mrow»«mn»1«/mn»«mo»+«/mo»«msup»«mrow»«mi»x«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«/mrow»«/mfrac»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mrow»«mo»+«/mo»«mi»c«/mi»«/math»'/> Þ <img src="data:image/png;base64,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" class="Wirisformula" alt="y equals fraction numerator 1 over denominator 2 end fraction log subscript e end subscript invisible function application left parenthesis 1 plus x to the power of 2 end exponent right parenthesis plus c" width="159" height="35" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mi»y«/mi»«mo»=«/mo»«mfrac»«mrow»«mn»1«/mn»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/mfrac»«mrow»«mrow»«msub»«mrow»«mi»log«/mi»«/mrow»«mrow»«mi»e«/mi»«/mrow»«/msub»«/mrow»«mo»⁡«/mo»«mrow»«mo»(«/mo»«/mrow»«/mrow»«mn»1«/mn»«mo»+«/mo»«msup»«mrow»«mi»x«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«mo»)«/mo»«mo»+«/mo»«mi»c«/mi»«/math»'/>.

The solution of the differential equation <img src="data:image/png;base64,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" class="Wirisformula" alt="left parenthesis 1 plus x to the power of 2 end exponent right parenthesis fraction numerator d y over denominator d x end fraction equals x" width="113" height="35" style="vertical-align:-12px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mo»(«/mo»«mn»1«/mn»«mo»+«/mo»«msup»«mrow»«mi»x«/mi»«/mrow»«mrow»«mn»2«/mn»«/mrow»«/msup»«mo»)«/mo»«mfrac»«mrow»«mi»d«/mi»«mi»y«/mi»«/mrow»«mrow»«mi»d«/mi»«mi»x«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mi»x«/mi»«/math»'/> is

Solution for the question - the solution of the differential equation (1+x^(2))(dy)/(dx)=x is y=-(1)/(2)log_(e)(1+x^(2))+c '/>   y=(1)/(2)log_(e)(1+x^(2))+c '/>

The solution of the differential equation (1+x^(2))(dy)/(dx)=x -Turito

Let f : R → R such that for all ‘x’ and y in R <img src="data:image/png;base64,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" class="Wirisformula" alt="vertical line f left parenthesis x right parenthesis minus f left parenthesis y right parenthesis vertical line less or equal than vertical line x minus y vertical line to the power of 3 end exponent text  then  end text f left parenthesis x right parenthesis" width="227" height="20" style="vertical-align:-4px" role="math" data-mathml='«math xmlns=¨http://www.w3.org/1998/Math/MathML¨ »«mo»|«/mo»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«mo»-«/mo»«mi»f«/mi»«mo»(«/mo»«mi»y«/mi»«mo»)«/mo»«mo»|«/mo»«mo»≤«/mo»«mo»|«/mo»«mi»x«/mi»«mo»-«/mo»«mi»y«/mi»«msup»«mrow»«mo»|«/mo»«/mrow»«mrow»«mn»3«/mn»«/mrow»«/msup»«mtext» then «/mtext»«mi»f«/mi»«mo»(«/mo»«mi»x«/mi»«mo»)«/mo»«/math»'/>

Solution for the question - let f : r r such that for all x and y in r |f(x)-f(y)| ^(@)c^(')(constan) '/>   x '/>   e^(-x) '/>   e^(x) '/>

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The solution of the differential equation is

The correct answer is:

The given equation is of the form. So, I.F.= Hence required solution Þ Þ .

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