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.
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!