$\frac{dy}{dx}+\sin(\frac{x+y}{2})=\sin(\frac{x-y}{2})$ Hello Mathematicians I am stuck at a differential equation problem 
$$\frac{dy}{dx}+\sin(\frac{x+y}{2})=\sin(\frac{x-y}{2})$$
I don't know here where to begin with.In other kind of problem I have seen I could have substituted $$x+y=k$$ and then $$1+\frac{dy}{dx}=\frac{dk}{dx}$$ 
but here i am also stuck with $x-y$ so above method cannot be used , can you give some hints here?

$\frac{dy}{dx}+\sin(\frac{x+y}{2})=\sin(\frac{x-y}{2})$
write 
$\sin(\frac{x+y}{2})=sin(\frac{x}{2})cos(\frac{y}{2})+cos(\frac{x}{2})sin(\frac{y}{2})$
similarly on R.H.S
terms cancel out and you get Variable seperable form!
