We consider the following model governing the temperature within the conducting I Beam: Uxx, 0 < x <1, t>0 Ut = BC : u(0,t) = 1, ur (1,t) = 2 IC : u(x, 0) = 2x (a) Determine a steady solution w(x) to the PDE and boundary conditions. (b) Let u(x,t) = w(x) + v(x,t) and identify the PDE, BC and IC satisfied by v(x,t). (c) Use the method of separation of variables to solve the above boundary value problem for v(x, t) and from this determine the solution u(x, t).