# 1D heat equation with non-homogenous boundary conditions

Please see the attached file for the fully formatted problem.

Solve the heat equation

u_t =a^2 * u_xx

for 0<x<L

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.

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#### Solution Summary

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.

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