Consider the plane-wall problem given by at where t is temperature, 0 is time. Boundary conditions are Initial condition is : k 2t x 0xL t(0,0) = to t(L, 0) = t t(x,0) = t(0)(x) Assuming that t(x, 0) = a(x) + b(0) + u(x, 0). Our goal is to choose a (x) and b(0) so that the problem for u(x, 0) will be homogeneous. (a) Determine the differential equations and the boundary and/or initial conditions that a(x), b(0) and u(x,0) must satisfy. (b) Solve for a(x) and b(0). (c) Determine the steady-state solution u(x, 0)