1- Solve the following heat problem with a constant heat source S (a positive constant), and boundary conditions as stated below: du(x, t) azu(x, t) = k OSXSL, t>0 at ax2 + S, u(0, t) = A u(L, t) = A u(x, 0) = A -7x X This equation has non-homogeneous PDE and BCs. Solving it requires several steps: a) Define the equilibrium (steady-state) problem and find the equilibrium temperature uE(x) (equilibrium means Ou / ot = 0). - Make a sketch of uE(x). b) Define the transient problem and find its solution ur(x, t). You should get the following PDE Jur(x,t) = k azur(x,t) at 3x2 with corresponding homogeneous BCS c) Find the general solution u(x, t) to the original problem (at this stage apply initial condition to find the coefficients)