Question

Solution of the differential equation $ \frac{dy}{dx}\tan y=\sin (x+y)+\sin (x-y) $ is:

• A. $ sec\text{ }y+2\text{ }cos\text{ }x=c $
• B. $ sec\text{ }y-2\text{ }cos\text{ }x=c $
• C. $ cos\text{ }y-2\text{ }sin\text{ }x=c $
• D. $ tan\text{ }y-2\text{ }sec\text{ }y=c $
• E. $ sec\text{ }y+2\text{ }sin\text{ }x=c $

Answer 1

Answer: (A)

$ \because $ $ \frac{dy}{dx}\tan y=\sin (x+y)+\sin (x-y) $
$ \Rightarrow $ $ \frac{dy}{dx}\tan y=2\sin x\,\cos y $
$ \Rightarrow $ $ \int{\tan y\,\sec y\,dy}=2\int{\sin x\,dx} $
$ \Rightarrow $ $ \sec y+2\cos x=c $