Consider the heat equation -. 8H 8'?! . = 77 CT cir- for the rod of length 5 with the prescribed temperatures at the end points \"(0, 3') = 8 and \"(5, 3') = 3. The initial condition is set at 0 temperature. (a) Which parts of the initial-boundary value problem are linear and nonhomogeneous'? (b) True or False: If \"1 is a solution of the same initial-value problem with H1110,\" = 8. \"1(5, r) = 0 and H2 is a solution of the same initial-value problem with H2 (0, I) = 0, 1:2(5, I) = 3, then H1 + H2 solves the given initial-boundary value problem. (6) Find the time-independent (steady state) solution of the given boundary-value problem for the given heat equation. (A) The boundary conditions (B) The initial condition (C) The heat equation