Differential Equations Question 31
Question: The general solution of the differential equation $ \frac{dy}{dx}=\cot x\cot y $ is
[AISSE 1983; MP PET 1994]
Options:
A) $ \cos x=c\cos ecy $
B) $ \sin x=c\sec y $
C) $ \sin x=c\cos y $
D) $ \cos x=c\sin y $
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Answer:
Correct Answer: B
Solution:
$ \frac{dy}{dx}=\cot x\cot y $
Therefore $ \int _{{}}^{{}}{\tan ydy=\int _{{}}^{{}}{\cot xdx}} $
Therefore $ \log \sec y=\log \sin x+\log c $
Therefore $ \sec y=c\sin x $ or $ c\sec y=\sin x $ .
BETA
