Consider the following non-homogenous heat equation on
with
Find a solution of the form
where are the eigenfunctions of an appropriate homogenous problem, and find explicit expressions for
Okay, ignore this last post. I have a different method....
Let
Then
and
Sub these back into the PDE to obtain
Choose
So
??
Also since we have
which is homogeneous.
Then we have
with .
Since this is homogenous, we can solve by letting
but now I get a little lost.....I think I know where to go, just not exactly how to get there. Already have calculated that , which will lead to what I need to prove (I think).