Question

Anyone here know how to do wave equations using PDE's? I'm really stuck on this problem. The conditions are:
1) du/dx (partial derivative) @ x=0 equals 0
2) du/dx (partial derivative) @ x=L equals 0
3) u(x,0)=x
4) du/dt (partial derivative) @ t=0 equals 0

Answer 1

What do you mean by 'do'?
I vaguely remember working out Fourier Series Expansions for the wave equation....
Lemme format what you have really quickly so it's easier to read.

Answer 2

Yeah, just Fourier series expansions.

Answer 3

\[\Large\rm u_{tt}=c^2 u_{xx}\]With conditions:\[\Large\rm u_x(0,t)=u_x(L,t)=0\]\[\Large\rm u_t(x,0)=0\]\[\Large\rm u(x,0)=x\]

Answer 4

Let's assume U = X*T,