Question: Solve the wave equation given the following boundary conditions.

u(0,t)=0

u(L,t)=0

u(x,0)=0

du/dt|t=0= x(L-x)

Attempt:

ok i'm not gonna write out all the steps because i can't use latex and it will be really messy, but i have

un= [Ancos(nπαt/L) + Bnsin(nπαt/L)]sin(nπx/L)

u(x,t) = Σ un

u(x,0) = ΣAnsin(nπx/L) = 0

Question:Does this make An=0?