Question

Reduce to two ordinary differential equations, one an eigenvalue problem, the other having one initial condition, and find the particular solution:

a) {partial^2 u}/{partial t^2} - {partial^2 u}/{partial x^2}- u = 0
For 0 < x < 1; t > 0; {partial u}/{partial x} (x,0) = 0
u(0,t) = u(1,t) = 0; u(x,0)= f(x)