Chapter 13.1, Problem 28E

To determine

To verify: The differential equation $\frac{{\partial }^{2}u}{\partial r^2}+\frac{1}{r}\frac{\partial u}{\partial r}+\frac{1}{r^2}\frac{{\partial }^{2}u}{\partial {\theta }^2}=0$ has solution $u=\left(c_1\cos \alpha \theta +c_2\sin \alpha \theta \right)\left(c_3{r}^{\alpha }+c_4{r}^{-\alpha }\right)$.