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Potential Equation on a Disc : Dirichlet

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Solve the potential equation on a disc...
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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 ...

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