Chapter 13, Problem 20RE

To determine

The steady state temperature $u\left(r,z\right)$ such that $\frac{{\partial }^{2}u}{\partial r^2}+\frac{1}{r}\frac{\partial u}{\partial r}-\frac{u}{r^2}+\frac{{\partial }^{2}u}{\partial z^2}=0,u\left(1,z\right)=0,u\left(r,0\right)=0\text{ and }u\left(r,1\right)=r-r^3$.