(Two steady state problems) Let u(x, t) denote the temperature in a metal rod of length L, with thermal conductivity Ko> 0 and thermal diffusivity k > 0. The rod has uniform cross-sectional area, and is insulated on its sides. The rod experiences non-uniform internal heating of the form Q(x) = Mx/L, for 0 < x < L, where M> 0 is a positive constant. The governing equation for u(x, t), the temperature of the rod, is the heat equation du Ju t x (*) The rod is subject to boundary conditions at each end of the rod. Two sets of possible boundary conditions are: = k +M 0