Differential Equations Question 39
Question: The solution of differential equation $ dy-\sin x\sin ydx=0 $ is
[MP PET 1996]
Options:
A) $ {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 $
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Answer:
Correct Answer: A
Solution:
$ \int _{{}}^{{}}{\frac{dy}{\sin y}}=\int _{{}}^{{}}{\sin xdx} $
Therefore $ \log \tan \frac{y}{2}=-\cos x+c $
Therefore $ \tan \frac{y}{2}={e^{-\cos x+c}} $
Therefore $ {e^{\cos x}}\tan \frac{y}{2}=e^{C}=c $ .
BETA
