Solve the PDE: (wave equation)

- Note some trick needs to be done with the (x^2) term to make it look homogeneous to carry through with separation of variables.

Utt - (c^2)(x^2)Uxx = 0

U(x,0) = 0

U(1,t) = 0
U(2,t) = 0

Ut(x,0) = f(x)


Thank you!