# Solving inhomogeneous PDEs

## Homework Statement

Hello, I'm having a problem solving second order inhomogeneous PDEs, for example the standard heat equation with a forcing term Sin(x)Sin(t) added onto it on the right hand side.

## Homework Equations

ut = uxx + Sin(ax)Sin(bt)

## The Attempt at a Solution

I can solve it for the homogeneous case using separation of variables, but where do I go from there? Thanks in advance.