I've just gotten back a corrected homework about differential equations, and now I need your help: Why is the ODE u''(x)=u(x)\sqrt{x} homogeneous, but the PDE $u_{xx}(x,y)+u_{yy}(x,y)e^{\sin x}=1$ is inhomogeneous? In both cases we have a function of $x$ that is not related to $u$, namely $e^{\sin x}$ and $\sqrt{x}$, don't we? So I'd think that both are inhomogeneous.
What am I doing wrong here?
Cheers, Marie :)