Potential Equation on a Disc : Dirichlet

Solution Preview

Please see the attached file for the complete solution.
Thanks for using BrainMass.

Solution:
We have to solve a Dirichlet problem inside a circle of radius (c).
The most usual method to do that is the Fourier method, that means using separation of variables.
Let's process our equation and let's separate the variables:
( 1)
Let
( 2)
Introducing in (1), we will have

( 3)
Why should we use a positive constant and not a negative one?
Because using a negative constant, the ODE in (T) doesn't have periodic solutions, while our problem must have periodic solutions with ...