Chapter 14.2, Problem 14E

To determine

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