Given $3u_{tt} + 10u_{xt} + 3u_{xx} = \sin(x+t)$ find the general solution.
I have yet to solve any inhomogeneous second order PDE (or even first order ones at that). For homogeneous PDE of same order, I managed to solve them by factoring the operators and so forth. Being new to PDEs (self studying via Strauss PDE book) I lack the intuition to find a clever way of solving these, however from my experience with ODEs I reckon there is a way to solve these by first solving the associated homogeneous first by factoring operators and so forth and stuff.. but not finding much progress on incorporating the $\sin(x+t)$ term.
Any help & direction to solving this would be greatly appreciated.