Nonhomogeneous PDEs

Whereas in solving nonhomogeneous ODEs involved first finding the complementary solution before making an Ansatz for the particular solution, for PDEs, we will instead make the Ansatz first.

This class deals with time-independent particular solutions, so we can Ansatz $u_p = h(x)$ meaning that the particular solution is some time-independent function $h(x)$. With the Ansatz, you can substitute it in and proceed with solving—later finding the complementary solution and proceeding as normal.