Differential Equations Question 8
Question: Solution of the equation $ \cos x\cos y\frac{dy}{dx}=-\sin x\sin y $ is
[DSSE 1987]
Options:
A) $ \sin y+\cos x=c $
B) $ \sin y-\cos x=c $
C) $ \sin y.\cos x=c $
D) $ \sin y=c\cos x $
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Answer:
Correct Answer: D
Solution:
$ \cos x\cos y\frac{dy}{dx}=-\sin x\sin y $
Therefore $ \frac{\cos y}{\sin y}dy=-\frac{\sin x}{\cos x}dx $
Therefore $ \cot ydy=-\tan xdx $
On integrating, we get $ \log \sin y=\log \cos x+\log c $
Therefore $ \sin y=c\cos x $ .
BETA
