Solution for the question - the solution of the differential equation x(dy)/(dx)=y(log y-log x+1) is y=ae^(-2//3(2a-x))sqrt(x+a) '/> y=ae^(2//3(2a+x))sqrt(x+a) '/>

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Question

The solution of the differential equation $square root of a plus x end root fraction numerator d y over denominator d x end fraction plus x y equals 0$ is

$y = A e^{2 / 3 (2 a - x) \sqrt{x + a}}$
$y = A e^{- 2 / 3 (a - x) \sqrt{x + a}}$
$y = A e^{2 / 3 (2 a + x) \sqrt{x + a}}$
$y = A e^{- 2 / 3 (2 a - x) \sqrt{x + a}}$

hint Hint:

Use the separation of variables technique to solve the equation.

The correct answer is: $y equals A e to the power of 2 divided by 3 left parenthesis 2 a minus x right parenthesis square root of x plus a end root end exponent$

$square root of a plus x end root space fraction numerator d y over denominator d x end fraction space plus space x y space equals space 0 square root of a plus x end root space fraction numerator d y over denominator d x end fraction space equals space minus x y square root of a plus x end root space d y space equals space minus x y space d x fraction numerator d y over denominator y end fraction space equals space fraction numerator negative x over denominator square root of a plus x end root space end fraction space d x I n t e g r a t i n g space b o t h space t h e space s i d e s comma integral fraction numerator d y over denominator y end fraction space equals space integral fraction numerator negative x over denominator square root of a plus x end root space end fraction space d x log y space equals space integral fraction numerator negative open parentheses x plus a minus a close parentheses over denominator square root of a plus x end root space end fraction space d x log y space equals negative 1 space open parentheses integral fraction numerator open parentheses x plus a close parentheses over denominator square root of a plus x end root space end fraction space d x space minus space integral fraction numerator a over denominator square root of a plus x end root space end fraction space d x close parentheses log y space equals space minus 1 open parentheses integral square root of x plus a end root space d x space minus a space integral fraction numerator 1 over denominator square root of a plus x end root space end fraction space d x close parentheses log y space equals space minus 1 open parentheses 2 over 3 open parentheses x plus a close parentheses to the power of 3 over 2 end exponent space minus 2 a square root of x plus a end root close parentheses space plus space log A space space space space space space space space space space space space space space space open parentheses w h e r e space A space i s space a n space a r b i t r a r y space c o n s tan t close parentheses log y space equals space space 2 a square root of x plus a end root space minus space 2 over 3 open parentheses x plus a close parentheses to the power of 3 over 2 end exponent space plus space log A log y space equals space 2 square root of x plus a end root open parentheses a space minus space fraction numerator open parentheses x plus a close parentheses over denominator 3 end fraction close parentheses space plus space log A log y space equals space 2 square root of x plus a end root open parentheses fraction numerator 3 a minus open parentheses x plus a close parentheses over denominator 3 end fraction close parentheses space plus space log A log y space equals space 2 over 3 square root of x plus a end root open parentheses 3 a minus x minus a close parentheses space plus space log A log y space equals 2 over 3 square root of x plus a end root open parentheses 2 a minus x close parentheses space plus space log A y space equals space e to the power of 2 over 3 open parentheses 2 a minus x close parentheses square root of x plus a end root end exponent space space plus space e to the power of log A end exponent therefore y space equals space A e to the power of 2 over 3 open parentheses 2 a minus x close parentheses square root of x plus a end root end exponent$

A differential equation is an equation which contains one or more terms and the derivatives of one variable (i.e., dependent variable) with respect to the other variable (i.e., independent variable) dy/dx = f(x)

The solution of $fraction numerator d to the power of 2 end exponent y over denominator d x to the power of 2 end exponent end fraction equals sec to the power of 2 end exponent invisible function application x plus x e to the power of x end exponent$ is

maths-General

General

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The solution of the differential equation $x fraction numerator d to the power of 2 end exponent y over denominator d x to the power of 2 end exponent end fraction equals 1$ , given that $y equals 1 comma fraction numerator d y over denominator d x end fraction equals 0$ when $x equals 1$ , is

maths-General

General

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Solution of $cos invisible function application x fraction numerator d y over denominator d x end fraction plus y sin invisible function application x equals 1$ is

maths-General

General

maths-

Integrating factor of $fraction numerator d y over denominator d x end fraction plus fraction numerator y over denominator x end fraction equals x to the power of 3 end exponent minus 3$ is

maths-General

General

maths-

Integrating factor of differential equation $cos invisible function application x fraction numerator d y over denominator d x end fraction plus y sin invisible function application x equals 1$ is

maths-General

General

maths-

The solution of the differential equation $fraction numerator d y over denominator d x end fraction plus y equals cos invisible function application x$ is

maths-General

General

maths-

The solution of the differential equation $fraction numerator d y over denominator d x end fraction plus fraction numerator y over denominator x end fraction equals x to the power of 2 end exponent$ is

maths-General

General

maths-

Solution of differential equation $fraction numerator d y over denominator d x end fraction equals fraction numerator y minus x over denominator y plus x end fraction$ is

maths-General

General

maths-

The solution of the equation $fraction numerator d y over denominator d x end fraction equals fraction numerator x over denominator 2 y minus x end fraction$ is

maths-General

General

maths-

The solution of the differential equation $fraction numerator d y over denominator d x end fraction equals fraction numerator x y over denominator x to the power of 2 end exponent plus y to the power of 2 end exponent end fraction$ is

maths-General

General

maths-

The solution of the differential equation $x d y minus y d x equals left parenthesis square root of x to the power of 2 end exponent plus y to the power of 2 end exponent right parenthesis end root d x$ is

maths-General

General

maths-

The solution of the equation $fraction numerator d y over denominator d x end fraction equals fraction numerator x plus y over denominator x minus y end fraction$ is

maths-General

General

maths-

The solution of $fraction numerator d y over denominator d x end fraction plus square root of open parentheses fraction numerator 1 minus y to the power of 2 end exponent over denominator 1 minus x to the power of 2 end exponent end fraction close parentheses end root equals 0$ is

maths-General

General

maths-

Solution of $y d x minus x d y equals x to the power of 2 end exponent y d x$ is

maths-General

General

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Solution of differential equation $fraction numerator d y over denominator d x end fraction equals 2 x y$ is

maths-General

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The solution of the differential equation is

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The solution of the differential equation $square root of a plus x end root fraction numerator d y over denominator d x end fraction plus x y equals 0$ is

The correct answer is: $y equals A e to the power of 2 divided by 3 left parenthesis 2 a minus x right parenthesis square root of x plus a end root end exponent$

The solution of $fraction numerator d to the power of 2 end exponent y over denominator d x to the power of 2 end exponent end fraction equals sec to the power of 2 end exponent invisible function application x plus x e to the power of x end exponent$ is

The solution of $fraction numerator d to the power of 2 end exponent y over denominator d x to the power of 2 end exponent end fraction equals sec to the power of 2 end exponent invisible function application x plus x e to the power of x end exponent$ is

The solution of the differential equation $x fraction numerator d to the power of 2 end exponent y over denominator d x to the power of 2 end exponent end fraction equals 1$ , given that $y equals 1 comma fraction numerator d y over denominator d x end fraction equals 0$ when $x equals 1$ , is

The solution of the differential equation $x fraction numerator d to the power of 2 end exponent y over denominator d x to the power of 2 end exponent end fraction equals 1$ , given that $y equals 1 comma fraction numerator d y over denominator d x end fraction equals 0$ when $x equals 1$ , is

Solution of $cos invisible function application x fraction numerator d y over denominator d x end fraction plus y sin invisible function application x equals 1$ is

Solution of $cos invisible function application x fraction numerator d y over denominator d x end fraction plus y sin invisible function application x equals 1$ is

Integrating factor of $fraction numerator d y over denominator d x end fraction plus fraction numerator y over denominator x end fraction equals x to the power of 3 end exponent minus 3$ is

Integrating factor of $fraction numerator d y over denominator d x end fraction plus fraction numerator y over denominator x end fraction equals x to the power of 3 end exponent minus 3$ is

Integrating factor of differential equation $cos invisible function application x fraction numerator d y over denominator d x end fraction plus y sin invisible function application x equals 1$ is

Integrating factor of differential equation $cos invisible function application x fraction numerator d y over denominator d x end fraction plus y sin invisible function application x equals 1$ is

The solution of the differential equation $fraction numerator d y over denominator d x end fraction plus y equals cos invisible function application x$ is

The solution of the differential equation $fraction numerator d y over denominator d x end fraction plus y equals cos invisible function application x$ is

The solution of the differential equation $fraction numerator d y over denominator d x end fraction plus fraction numerator y over denominator x end fraction equals x to the power of 2 end exponent$ is

The solution of the differential equation $fraction numerator d y over denominator d x end fraction plus fraction numerator y over denominator x end fraction equals x to the power of 2 end exponent$ is

Solution of differential equation $fraction numerator d y over denominator d x end fraction equals fraction numerator y minus x over denominator y plus x end fraction$ is

Solution of differential equation $fraction numerator d y over denominator d x end fraction equals fraction numerator y minus x over denominator y plus x end fraction$ is

The solution of the equation $fraction numerator d y over denominator d x end fraction equals fraction numerator x over denominator 2 y minus x end fraction$ is

The solution of the equation $fraction numerator d y over denominator d x end fraction equals fraction numerator x over denominator 2 y minus x end fraction$ is

The solution of the differential equation $fraction numerator d y over denominator d x end fraction equals fraction numerator x y over denominator x to the power of 2 end exponent plus y to the power of 2 end exponent end fraction$ is

The solution of the differential equation $fraction numerator d y over denominator d x end fraction equals fraction numerator x y over denominator x to the power of 2 end exponent plus y to the power of 2 end exponent end fraction$ is

The solution of the differential equation $x d y minus y d x equals left parenthesis square root of x to the power of 2 end exponent plus y to the power of 2 end exponent right parenthesis end root d x$ is

The solution of the differential equation $x d y minus y d x equals left parenthesis square root of x to the power of 2 end exponent plus y to the power of 2 end exponent right parenthesis end root d x$ is

The solution of the equation $fraction numerator d y over denominator d x end fraction equals fraction numerator x plus y over denominator x minus y end fraction$ is

The solution of the equation $fraction numerator d y over denominator d x end fraction equals fraction numerator x plus y over denominator x minus y end fraction$ is

The solution of $fraction numerator d y over denominator d x end fraction plus square root of open parentheses fraction numerator 1 minus y to the power of 2 end exponent over denominator 1 minus x to the power of 2 end exponent end fraction close parentheses end root equals 0$ is

The solution of $fraction numerator d y over denominator d x end fraction plus square root of open parentheses fraction numerator 1 minus y to the power of 2 end exponent over denominator 1 minus x to the power of 2 end exponent end fraction close parentheses end root equals 0$ is

Solution of $y d x minus x d y equals x to the power of 2 end exponent y d x$ is

Solution of $y d x minus x d y equals x to the power of 2 end exponent y d x$ is

Solution of differential equation $fraction numerator d y over denominator d x end fraction equals 2 x y$ is

Solution of differential equation $fraction numerator d y over denominator d x end fraction equals 2 x y$ is