The PDE

The PDE can be rewritten using this solution as (placing constants in the DE for Y) into

** Note: ** Use the prime notation for derivatives, so the derivative of

Since these differential equations are independent of each other, they can be separated

DE in X:

DE in Y:

Now we solve the separate separated ODEs for the different cases in

** Case 1: **

** DE in Y **

If

Integrating both sides with respect to

Solving for Y, using the funny algebra of constant where

For

** Case 2: **

** Case 3: **

** Final Solution **

** Case 1: **

** Case 2: **

** Case 3: **

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