. Inhomogeneous PDE and BCs:\ Consider the heat equation with a source\ ut =\ 1\ 3\ uxx + x(1 x) with u(0, t) = 0 and ux(1, t) = 1.\ (a) Give a physical interpretation of the boundary conditions.\ (b) Find the equilibrium solution, denoted by p(x), say; and plot it using Matlab or some\ other suitable plotting software.\ [To get you started, you may wish to use the given code hw3code.m, which plots the\ equilibrium solutions from Examples 2.2 and 2.3 of the textbook, as in Figure 2.3.]\ (c) Let u(x, t) = p(x) + v(x, t), where v(x, t) is the deviation from the equilibrium. Show\ that the function v(x, t) satisfies the associated homogeneous PDE and BCs