Use Fourier transforms to solve the PDE
, ,
subject to
.
ATTEMPT:
I took Fourier transforms in and got the ODE
.
Trying to solve this ODE I get
.
This results in there are three solutions to the ODE depending on the value of . Am I supposed find solve for all three solutions?
How can I proceed next?
Should I have taken Fourier transforms in instead in the first step?