The PDE is separable, so we look for solutions of the form
The PDE can be rewritten using this solution as
= =

Note: Use the prime notation for derivatives, so the derivative of is written as . Do NOT use

Since these differential equations are independent of each other, they can be separated
DE in X:
DE in T:

These are both separable ODE's. The DE in X we separate as

Integrate both sides, the constant of integration c going on the right side:
Using the funny constant algebra that , solving for X we get X =
Since the differential equation in Y is the same we get Y = .
Finally u = .