Differential Equations Question 75
Question: Solution of the differential equation $ \frac{dy}{dx}\tan y=\sin (x+y)+\sin (x-y) $ is
[Kerala (Engg.) 2005]
Options:
A) $ \sec y+2\cos x=c $
B) $ \sec y-2\cos x=c $
C) $ \cos y-2\sin x=c $
D) $ \tan y-2\sec y=c $
E) $ \sec y+2\sin x=c $
Show Answer
Answer:
Correct Answer: A
Solution:
$ \frac{dy}{dx}\tan y=\sin (x+y)+\sin (x-y) $
$ \frac{dy}{dx}(\tan y)=2\sin x\cos y $
Therefore $ \frac{\sin y}{{{\cos }^{2}}y}dy=2\sin xdx $
Therefore $ \int{\frac{\sin y}{{{\cos }^{2}}y}}dy=2\int{\sin xdx} $
Therefore $ \frac{1}{\cos y}=-2\cos x+c $
\ $ \sec y+2\cos x=c $ .
BETA
