$($c$)$ Solve the wave equation subject to the given conditions.

$a^2\frac{de{l}^{2}u}{del{x}^2}=\frac{de{l}^{2}u}{del{t}^2}$

Initial Conditions,

$u(0,t)=u(L,t)=0.$

Boundary Conditions

$u(x,0)=0,\frac{\text{d}\text{e}\text{l}\text{u}}{\text{d}\text{e}\text{l}\text{t}}{|}_t=0$