Use the method of eigenfunction expansion to solve with boundary conditions and initial condition
I think I might have stuffed my solution here, but I don't know.
Would someone please be able to help me out?
Base a trial solution on the solution to the homogeneous problem
Now represent as a series of the particular eigenfunctions
Sub into PDE
The only way for this to be true for all is if
This is a first order ODE.....so use an integrating factor
In order for choose
Skipping a few lines of calculation...