Question

Find the solution of $\frac{dy}{dx}+\sin \left(\frac{x+y}{2}\right)=\sin \left(\frac{x-y}{2}\right)$.

• A. $\log \tan \frac{y}{4}=c-2\sin \frac{x}{2}$
• B. $\log \tan \frac{y}{2}=c+2\sin \frac{x}{2}$
• C. $\log \tan \frac{y}{2}=c-2\sin \frac{x}{2}$
• D. $\log \tan \frac{y}{4}=c+2\sin \frac{x}{2}$

Answer 1

The correct option is A $\log \tan \frac{y}{4}=c-2\sin \frac{x}{2}$

$\frac{dy}{dx}+\sin \left(\frac{x+y}{2}\right)=\sin \left(\frac{x-y}{2}\right)$
or $\frac{dy}{dx}=\sin \left(\frac{x-y}{2}\right)-\sin \left(\frac{x+y}{2}\right)$
or $\frac{dy}{dx}=-2\cos \frac{x}{2}\sin \frac{y}{2}$
or $\int cosec\frac{y}{2}dy=\int -2\cos \frac{x}{2}dx$
or $\log \tan \frac{y}{4}=c-2\sin \frac{x}{2}$