Solving the 2D Laplace Equationd Approach

[Uku]

Homework Statement

$$u_{tt}=u_{xx}$$

The Attempt at a Solution

Where do I start? I have this wonderful Schaums outline at hand, and by looking at similar (unfortunately unsolved problems) I can guess that the answer will be in the range of:

$$u=F(x+iy)+G(x-iy)$$

I'm saying something in that range (solution of the 2D Laplace equation), but not exactly.

 

[Uku]

Hoi! It is 2am and I was rushing things a bit. I have yet another book which has the solution for the 2D Laplace equation. So in my case I just have to take

$$1-\lambda^{2}$$

Instead of

$$1+\lambda^{2}$$

as presented in the Laplace equation solution?
I'm assuming here that the procedure of solving the Laplace equation is known to the reader. Sorry for that.

Regards,
Uku