$2-$ Show that the temperature distribution through the rectangular rod shown in the figure is given by:

$\frac{T(x,y)}{q^{\text{'}\text{'}\text{'}}\frac{l^2}{2}k}=1-(\frac{y}{l}{)}^2+\frac{32}{{}^3}{\displaystyle \underset{n=0}{\overset{}{}}}\frac{(-1{)}^{n+1}cos[(2n+1)\frac{}{2}\frac{y}{l}]cosh[(2n+1)\frac{}{2}\frac{x}{L}]}{(2n+1{)}^{3}cosh[(2n+1)\frac{}{2}\frac{L}{l}]}$