Solution of differential equation $s e c x d y - c o s e c y d x = 0$ is

c o s x + s i n y = c

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s i n x + c o s y = c

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s i n y - c o s x = c

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c o s y - s i n x = c

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Solution

The correct option is B $s i n x + c o s y = c$
$s e c x d y - c o s e c y - d x = 0$
$\frac{d y}{c o s x} = \frac{d x}{s i n y}$
By variable separable from
$s i n y d y = c o s x d x$
integrating,
$\int s i n y d y = \int c o s x d x$
$- c o s y = s i n x + c$
$s i n x + c o s y + c = 0$
or
$s i n x + c o s y = c$

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