Chapter 14.2, Problem 6E

The displacement u(x, t) of a string that is driven by an external force is determined from

$\frac{{\partial }^{2}u}{\partial x^2}+\sin \pi x\sin \omega t=\frac{{\partial }^{2}u}{\partial t^2},0<x<1,t>0$

u(0, t) = 0, u(1, t) = 0, t > 0

$u(x,0)=0,{\frac{\partial u}{\partial t}|}_{t-0}=0,0<x<1$.

Solve for u(x, t).