Solution of 2y sin x(dy)/(dx)=2sin x cos x-y^(2)cos x,x=(pi)/-Turito

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Solution of $2 y sin space x fraction numerator d y over denominator d x end fraction equals 2 sin space x cos space x minus y squared cos space x comma x equals pi over 2 comma y equals 1$ is given by

$y^{2} = \sin x$
$y = \sin^{2} x$
$y^{2} = \cos x + 1$
None of these

Hint:

In this question, we will integrate the equation then after putting the value of x and y we will get the value of constant.

The correct answer is: $y squared equals sin space x$

$G i v e n comma space 2 y sin space x fraction numerator d y over denominator d x end fraction equals 2 sin space x cos space x minus y squared cos space x rightwards double arrow 2 y sin space x fraction numerator d y over denominator d x end fraction plus y squared cos space x equals sin 2 x rightwards double arrow 2 sin x fraction numerator d over denominator d x end fraction y squared minus y squared fraction numerator d over denominator d x end fraction sin x equals sin 2 x rightwards double arrow y squared fraction numerator d over denominator d x end fraction sin x space equals sin 2 x i n t e g r a t i n g space b o t h space s i d e s comma integral sin x space y squared space d x space equals integral sin 2 x space d x rightwards double arrow sin x space y squared equals fraction numerator negative cos 2 x over denominator 2 end fraction plus C N o w comma space f o r space x equals straight pi over 2 comma space y equals 1 rightwards double arrow sin straight pi over 2.1 squared equals fraction numerator negative cos 2 begin display style straight pi over 2 end style over denominator 2 end fraction plus C rightwards double arrow C equals 1 plus open parentheses fraction numerator negative 1 over denominator 2 end fraction close parentheses rightwards double arrow C equals 1 half sin x. y squared equals fraction numerator negative cos 2 x over denominator 2 end fraction plus 1 half rightwards double arrow y squared equals fraction numerator 1 minus cos 2 x over denominator 2 sin x end fraction$

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Solution of $2 y sin space x fraction numerator d y over denominator d x end fraction equals 2 sin space x cos space x minus y squared cos space x comma x equals pi over 2 comma y equals 1$ is given by

$y^{2} = \sin x$
$y = \sin^{2} x$
$y^{2} = \cos x + 1$
None of these

The correct answer is: $y squared equals sin space x$

Equation of the curve passing through (3, 9) which satisfies the differential equation $fraction numerator d y over denominator d x end fraction equals x plus 1 over x squared$ is

Equation of the curve passing through (3, 9) which satisfies the differential equation $fraction numerator d y over denominator d x end fraction equals x plus 1 over x squared$ is

If $f left parenthesis x right parenthesis space equals space f apostrophe left parenthesis x right parenthesis$ and f(1) = 2, then f(3) =

If $f left parenthesis x right parenthesis space equals space f apostrophe left parenthesis x right parenthesis$ and f(1) = 2, then f(3) =

The degree and order of the differential equation of all tangent lines to the parabola x² = 4y is :

The degree and order of the differential equation of all tangent lines to the parabola x² = 4y is :

If the algebraic sum of distances of points (2, 1) (3, 2) and (-4, 7) from the line y = mx + c is zero, then this line will always pass through a fixed point whose coordinate is

If the algebraic sum of distances of points (2, 1) (3, 2) and (-4, 7) from the line y = mx + c is zero, then this line will always pass through a fixed point whose coordinate is

A particle moves in a straight line with velocity given by $fraction numerator d x over denominator d t end fraction equals x plus 1$ (x being the distance described). The time taken by the particle to describe 99 metres is :

A particle moves in a straight line with velocity given by $fraction numerator d x over denominator d t end fraction equals x plus 1$ (x being the distance described). The time taken by the particle to describe 99 metres is :

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