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Question

An integrating factor of the differential equation $x fraction numerator d y over denominator d x end fraction plus y to the power of 1 end exponent o g x equals x e to the power of x end exponent x to the power of negative fraction numerator 1 over denominator 2 end fraction 1 o g x end exponent comma$ $left parenthesis x greater than 0 right parenthesis$ is

$x (y + c o s x) = s i n x + c$
$x (y - c o s x) = s i n x + c$
$x (y \cdot c o s x) = s i n x + c$
$x (y - c o s x) = c o s x + c$

The correct answer is: $x left parenthesis y plus blank c o s blank x right parenthesis equals blank s i n blank x plus c$

Related Questions to study

The solution of the differential equation $fraction numerator d y over denominator d x end fraction plus fraction numerator 3 x to the power of 2 end exponent over denominator 1 plus x to the power of 3 end exponent end fraction y equals fraction numerator s i n to the power of 2 end exponent x over denominator 1 plus x to the power of 3 end exponent end fraction$ is

For such questions, we should know different methods to solve differential equation.

The solution of the differential equation $fraction numerator d y over denominator d x end fraction plus fraction numerator 3 x to the power of 2 end exponent over denominator 1 plus x to the power of 3 end exponent end fraction y equals fraction numerator s i n to the power of 2 end exponent x over denominator 1 plus x to the power of 3 end exponent end fraction$ is

For such questions, we should know different methods to solve differential equation.

The solution of $left parenthesis x minus y to the power of 3 end exponent right parenthesis d x plus 3 x y to the power of 2 end exponent d y equals 0$ is

The solution of $left parenthesis x minus y to the power of 3 end exponent right parenthesis d x plus 3 x y to the power of 2 end exponent d y equals 0$ is

$y equals fraction numerator x over denominator x plus 1 end fraction$ is a solution of the differential equation —.

For such questions, we should know different method to solve differential equation.

$y equals fraction numerator x over denominator x plus 1 end fraction$ is a solution of the differential equation —.

For such questions, we should know different method to solve differential equation.

parallel

The degree of the differential equation $y left parenthesis x right parenthesis equals 1 plus fraction numerator d y over denominator d x end fraction plus fraction numerator 1 over denominator 1.2 end fraction left parenthesis fraction numerator d y over denominator d x end fraction right parenthesis to the power of 2 end exponent plus fraction numerator 1 over denominator 1.2.3 end fraction left parenthesis fraction numerator d y over denominator d x end fraction right parenthesis to the power of 3 end exponent plus$ is

For such questions, we should know the definition of power.

The degree of the differential equation $y left parenthesis x right parenthesis equals 1 plus fraction numerator d y over denominator d x end fraction plus fraction numerator 1 over denominator 1.2 end fraction left parenthesis fraction numerator d y over denominator d x end fraction right parenthesis to the power of 2 end exponent plus fraction numerator 1 over denominator 1.2.3 end fraction left parenthesis fraction numerator d y over denominator d x end fraction right parenthesis to the power of 3 end exponent plus$ is

For such questions, we should know the definition of power.

If $left parenthesis fraction numerator 2 plus blank s i n blank x over denominator 1 plus y end fraction right parenthesis fraction numerator d y over denominator d x end fraction equals negative blank c o s blank x comma$ $y left parenthesis 0 right parenthesis equals 1$ , then $y left parenthesis fraction numerator pi over denominator 2 end fraction right parenthesis equals$

If $left parenthesis fraction numerator 2 plus blank s i n blank x over denominator 1 plus y end fraction right parenthesis fraction numerator d y over denominator d x end fraction equals negative blank c o s blank x comma$ $y left parenthesis 0 right parenthesis equals 1$ , then $y left parenthesis fraction numerator pi over denominator 2 end fraction right parenthesis equals$

The differential equation $fraction numerator d to the power of 2 end exponent y over denominator 2 end fraction plus x fraction numerator d y over denominator d x end fraction plus blank s i n blank y plus x to the power of 2 end exponent equals 0$ is of the $d x$ following type

The differential equation $fraction numerator d to the power of 2 end exponent y over denominator 2 end fraction plus x fraction numerator d y over denominator d x end fraction plus blank s i n blank y plus x to the power of 2 end exponent equals 0$ is of the $d x$ following type

parallel

The point of intersection of tangents at the ends of the latus rectum of the parabola $y to the power of 2 end exponent equals 4 x text is equal to end text$

The point of intersection of tangents at the ends of the latus rectum of the parabola $y to the power of 2 end exponent equals 4 x text is equal to end text$

The equation of family of curves for which the length of the normal is equal to the radius vector is

The equation of family of curves for which the length of the normal is equal to the radius vector is

The general solution of $y to the power of 2 end exponent d x plus left parenthesis x to the power of 2 end exponent minus x y plus y to the power of 2 end exponent right parenthesis d y equals 0$ is

The general solution of $y to the power of 2 end exponent d x plus left parenthesis x to the power of 2 end exponent minus x y plus y to the power of 2 end exponent right parenthesis d y equals 0$ is

parallel

The curve satisfying $y equals 2 x fraction numerator d y over denominator d x end fraction$ is a

The curve satisfying $y equals 2 x fraction numerator d y over denominator d x end fraction$ is a

The differential equation of the family of curves $c y to the power of 2 end exponent equals 2 x plus c comma$ where $c$ is an arbitrary constant is

The differential equation of the family of curves $c y to the power of 2 end exponent equals 2 x plus c comma$ where $c$ is an arbitrary constant is

$text The line end text x minus y plus 2 equals 0 text touches the parabola end text y to the power of 2 end exponent equals 8 x text at the end text$ point

$text The line end text x minus y plus 2 equals 0 text touches the parabola end text y to the power of 2 end exponent equals 8 x text at the end text$ point

parallel

The solution of the differential equation $fraction numerator d y over denominator d x end fraction equals fraction numerator y over denominator x end fraction plus fraction numerator f comma left parenthesis fraction numerator y over denominator x end fraction right parenthesis over denominator empty set left parenthesis fraction numerator y over denominator x end fraction right parenthesis end fraction$ is

The solution of the differential equation $fraction numerator d y over denominator d x end fraction equals fraction numerator y over denominator x end fraction plus fraction numerator f comma left parenthesis fraction numerator y over denominator x end fraction right parenthesis over denominator empty set left parenthesis fraction numerator y over denominator x end fraction right parenthesis end fraction$ is

Solution of $fraction numerator x d y over denominator x to the power of 2 end exponent plus y to the power of 2 end exponent end fraction equals left parenthesis fraction numerator y over denominator x to the power of 2 end exponent plus y to the power of 2 end exponent end fraction 1 right parenthesis d x$ is

Solution of $fraction numerator x d y over denominator x to the power of 2 end exponent plus y to the power of 2 end exponent end fraction equals left parenthesis fraction numerator y over denominator x to the power of 2 end exponent plus y to the power of 2 end exponent end fraction 1 right parenthesis d x$ is

The angle between the tangents drawn at the end points of the latus rectum of parabola $y to the power of 2 end exponent equals 4 a x text is end text$

The angle between the tangents drawn at the end points of the latus rectum of parabola $y to the power of 2 end exponent equals 4 a x text is end text$

parallel

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