Solution of differential equation dy- sin x sin ydx=0 is :

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Solution of differential equation $d y - \sin x \sin y d x = 0$ is :

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$e^{\cos x} \tan \frac{y}{2} = c$

$\cos x \tan y = c$

$e^{\cos x} \tan y = c$

$\cos x \sin y = c$

answer is C.

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Detailed Solution

Given $d y - \sin x \sin y d x = 0$

$\Rightarrow d y = \sin x \sin y d x$

Dividing the L.H.S. and R.H.S. by sin y We get:

$cosec y d y = \sin x d x$

Integrating on both sides we get:

$\Rightarrow \log \tan y / 2 = c - \cos x$

Note $: \log x = y \Rightarrow x = e^{y}$

So, $\tan y / 2 = e^{c} \cdot e^{- \cos x}$

$\Rightarrow e^{\cos x} \tan \frac{y}{2} = e^{c} = c^{'} .$

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