1. The problem statement, all variables and given/known data By trial and error, find a solution of the diffusion equation du/dt = d^2u / dx^2 with the initial condition u(x, 0) = x^2. 2. Relevant equations 3. The attempt at a solution Given the initial condition, I tried finding a solution at the steady state (du/dt=0) which gives me d^2u / dx^2 = 0, from I found u(x,0)=c_1 + c_2 x = x^2 and now I am stuck. Thanks in advance!