Consider the solution of the inhomogeneous heat equation It 20u = + x, 2 over the...

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Consider the solution of the inhomogeneous heat equation It 20u = + x, 2 over the interval 0 < x < L with boundary conditions u(0,t) = 0 and u(L,t) = 0. (a) (b) (c) Determine the equilibrium solution as t . Next assume the initial condition u(x, t = 0) = 1 for 0 < x < L. Determine the solution for t > 0. Express your solution as a sum of the equilibrium solution plus a series using an appropriate set of eigenfunctions. Suppose the boundary condition is now changed to (0,t) = 0 (L,t) = B. For what value of will an equilibrium solution exist? Consider the solution of the inhomogeneous heat equation It 20u = + x, 2 over the interval 0 < x < L with boundary conditions u(0,t) = 0 and u(L,t) = 0. (a) (b) (c) Determine the equilibrium solution as t . Next assume the initial condition u(x, t = 0) = 1 for 0 < x < L. Determine the solution for t > 0. Express your solution as a sum of the equilibrium solution plus a series using an appropriate set of eigenfunctions. Suppose the boundary condition is now changed to (0,t) = 0 (L,t) = B. For what value of will an equilibrium solution exist?