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

Chapter 15, Problem 6

(choose chapter or problem)

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,   \(\left.\quad \frac{\partial u}{\partial t}\right|_{t=0}=0\),   0<x<1

Solve for u(x, t).