The PDE can be rewritten using this solution as

** 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 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

Since the differential equation in Y is the same we get Y =

Finally u =