Expand all variables in the problem for u in a Fourier series:
Put into P.D.E. utt = a2 uxx:
Because of the choice of the Xn:
Put into I.C.s u(x,0) = f(x) and ut(x,0) = g(x):
Solve this O.D.E. and initial condition for Cn:
Characteristic polynomial:
Initial conditions: