Question: 1. Apply separation of variables to solve the following mixed boundary value problem:
2. Solve for the steady-state temperature distribution in a thin flat plate covering the rectangle 0 ≤ x ≤ a, 0 ≤ y ≤ b if the temperature on the vertical sides and bottom side are kept at zero, and the temperature along the top side is
f(x) = x(x - a)2