Trying to get this PDE in terms of 'y'

[hunt_mat]

Go back to the original equations:
$$X''(x)+\lambda^{2}X(x)=0,\quad T''(t)+\lambda^{2}T(t)=0$$
What are the solutions to these equations?

 

[HallsofIvy]

An n^th order ordinary differential equation always involves n unknown constants. An n^th order partial differential equation always involves n unknown functions.

I pretty much told you before that the general solution to that differential equation is
y= F(x- vt)+ G(x+ vt) where F and G are arbitrary, twice differentiable, functions.

The simple fact is that you are trying to do a problem that is far beyond your knowledge. If you do not know how to solve basic ordinary differential equations, no one is going to be able to tell you how to solve partial differential equations in a few sentences.

 

[timthereaper]

I agree with Ivy. Everyone here is trying to help you (the OP) solve the problem, but it's your inexperience that's stopping you from understanding the solution process. PDEs are fairly difficult to solve a lot of the time even for people with a fair amount of math under their belt. I do appreciate your bravado in tackling the wave equation and applaud your desire to extend your mathematical prowess, however I think you should spend a bit more time learning the fundamentals.

It's for a physics paper I'm working on; I don't need to understand all the mathematical concepts, I just need the equation solved for y please.

About this, you can't just expect to post a problem and get a detailed solution back. It doesn't work that way. IMHO, the forums are really an aid to your own problem solving. If you're looking for the other kind of problem solving, try http://www.wolframalpha.com/" .