Consider the steady state temperature distribution on a rectangular metal plate with dimensions $2m1m,$ and boundary temperature as shown in Figure below. Within the plate, there is a heat generation $q^{}=6[\frac{W}{m^3}].$ The plate has the thermal conductivity of $k=3[\frac{W}{m^o}C].$

a$.$ Specify the partial differential equation and the boundary conditions that define the problem.

b$.$ Using the separation$-$of$-$variables technique, find the analytical expression for the temperature distribution, $T(x,y),$ in the metal plate.