The 1-dimensional heat equation is given as follows: du d'u dt - =k- for all 0xL and t>0 dx Deduce the solution to the above differential equation, subjected to the following boundary and initial conditions: u(0,t)=0 for all t > 0, u(L,t)=0 for all t > 0, u(x,0) = 20 for all 0xL. (iii)