The general solution of differential equation $(cos x - y) d y = y sin x d x$ is

y s i n x = y^{2} + c

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y c o s x = y^{2} + c

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2 y s i n x = y^{2} + c

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2 y c o s x = y^{2} + 2 c

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Solution

The correct option is C $y c o s x = y^{2} + c$
Given differential equation is
$(c o s x - y) d y = y s i n x d x$

$c o s x d y - y d y = y s i n x d x$

$c o s x d y - y s i n x d x = y d y$

$d (y c o s x) = y d y$

integrating both side

$\int d (y c o s x) = \int y d y$

$y c o s x = \frac{y^{2}}{2} + c$
Which is the required general solution.

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