E$5.$ Derive an expression for the temperature distribution in a plane wall in which there are uniformly distributed heat sources that vary according to the linear relation

$q_G^{}=q_w^{}[1-(T-T_w)]$

where $q_w^{}$ is a constant equal to the heat generation per unit volume at the wall temperature Tw$.$ Both sides of the plate are maintained at Tw and the plate thickness is $2$L$.$