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?

You are correct, as it is not a linear ODE, it is neither homogeneous nor inhomogeneous.
The cited characterization is most likely based on the fact that $y=0$ is a solution, but that is only a necessary condition for linearity, not a sufficient one.
