If utt - uxx= 1-x for 0<x<1, t>0
u(x,0) = x2(1-x) for 0≤x≤1
ut(x,)=0 for 0≤x≤1
The Attempt at a Solution
I was thinking to make a judicious change of variables that not only converts the PDE to a homogenous PDE, but also makes the boundary conditions homogenous.
I am quite unsure how to even start this problem...