I'm struggling with a second-year practice problem for partial DEs.
'Consider the one-dimensional wave equation u(tt) = c^2*u(xx) on the interval -L < x L with the boundary conditions u(x)(0,t) = u(x)(L,t) = 0.
a) Find the most general solution of the wave equation for these boundary conditions
b) Find the solution corresponding to the initial conditions u(x,0) = 0 and u(t)(x,0) = Kx(L-x) for positive constant K. '
I'm just looking for a guide for how to approach the problem; I'm lost at the moment.
Thanks in advance.