Please see the attached file for the fully formatted problem.
Solve the heat equation
u_t =a^2 * u_xx
under the conditions:
u(0,t)=1 u(L,t)=2 u(x,0)=0
Solve this problem by converting this problem into a problem with homogeneous boundary conditions. Show that as t approaches infinity the solution approaches the equilibrium solution.© BrainMass Inc. brainmass.com March 4, 2021, 9:25 pm ad1c9bdddf
The solution shows in full details how to convert the problem to a solvable homogeneous problem, solves it and then shows how it behaves at a steady state.