Homogeneous or non - homogeneous $?$ The second order differential equation is given by -
$ \frac{d^{2}y}{dx^{2}} + \sin (x+y) = \sin x$ 
Is this a homogeneous differential equation $?$
Well, I guess this is not a homogeneous differential equation since the form of this equation is not $a(x)y'' + b(x)y' +c(x)y = 0$.
But the answer is given that it's homogeneous. 
How can this equation be homogeneous?

Let $u=x+y$ ,
Then $\dfrac{du}{dx}=1+\dfrac{dy}{dx}$
$\dfrac{d^2u}{dx^2}=\dfrac{d^2y}{dx^2}$
$\therefore\dfrac{d^2u}{dx^2}+\sin u=\sin x$
This is a inhomogeneous differential equation.
