The solution of differential equation dy - x ydx = 0 is - Vidyadip

MCQ

The solution of differential equation $dy - \sin x\sin ydx = 0$ is

✓
${e^{\cos x}}\tan \frac{y}{2} = c$
B
${e^{\cos x}}\tan y = c$
C
$\cos x\tan y = c$
D
$\cos x\sin y = c$

✓

Answer

Correct option: A.

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

a
(a) $\int_{}^{} {\frac{{dy}}{{\sin y}}} = \int_{}^{} {\sin xdx} $ ==> $\log \tan \frac{y}{2} = - \cos x + c$

==> $\tan \frac{y}{2} = {e^{ - \cos x + c}}$ ==> ${e^{\cos x}}\tan \frac{y}{2} = {e^C} = c$.

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