Question

The general solution of the differential equation $\frac{dy}{dx} + \sin (x + y) = \sin (x -y) $ is

• A. $\log \tan y + \sin x = C$
• B. $\log \tan \frac{y}{2} + 2 \sin x = C $
• C. $ \tan \frac{y}{2} + \log \sin x = C $
• D. None of these

Answer 1

Answer: (B)

The equation is,
$\frac{d y}{d x}=\sin (x-y)-\sin (x +y)=2 \cos x \sin (-y)$
$\Rightarrow \frac{d y}{\sin y}+2 \cos x d x=0$
$\Rightarrow \int \text{cosec} y d y+2 \int \cos x d x=C$
$\Rightarrow \log \tan \frac{y}{2}+2 \sin x=C$