Finding the solution of the wave equation that satisfies the boundary conditions

[Jack_O]

1. The problem statement, all variables and given/known data

http://i36.photobucket.com/albums/e14/py07jo/Homework%20problems/9841e864.jpg

2. Relevant equations

N/A

3. The attempt at a solution


http://i36.photobucket.com/albums/e14/py07jo/Homework%20problems/8cf112dc.jpg

Really stuck with this, i can't work out how to apply the boundary conditions to generate the simultaneous equations to find the specific solution. Can't find any similar examples either.
Help appreciated.

[Tom Mattson]

Do you know D'Alambert's formula? It will give you the solution almost immediately!

[Jack_O]

Just looked it up on wikipedia but it confuses me, it doesn't explain it very well.

[Tom Mattson]

You need to translate their notation to yours. They put it thusly.

u_{tt}-c^2u_{xx}=0

The subscripts indicate partial differentiation, ie u_{tt}=\frac{\partial^2u}{\partial t^2}. So their g(x) equals your e^{-x^2} and their h(x) equals your 2cxe^{-x^2}. It's just plug and chug from there.