PDE Homework #3: Separation of Variables for the Heat Equation Use separation of variables to solve the following heat equation problem with inhomogeneous boundary conditions: 2 2 3 (0, ) 20 (40, ) 100 ( , 0) 40 u u t x u t u t u x x ? ? ? ? ??? ? ? After you have found the infinite series solution using separation of variables, then use Matlab to evaluate your series solution in order to plot the temperature profile at a few fixed values of time. In other words, plot u(x,t) versus x for a few fixed values of t. Put all the temperature curves on a single plot and label the t value for each curve.