What are the eigenfunctions and their frequencies of the vibrating string? Of the heat equation?

No clue how to start! Somehow I'm supposed to come up with:

W = [c(s)/x^3] + [x/(s^2(s+1))]

w(0,s) = 0
c(s) = 0
w(x,t) = x(t - 1 + e^-t)

Appreciate some help getting started.

Diolch yn fawr!