Chapter 12.1, Problem 28E

In Problems 27 and 28 show that the given partial differential equation possesses the indicated product solution.

28. $\frac{{\partial }^{2}u}{\partial r^2}+\frac{1}{r}\frac{\partial u}{\partial r}+\frac{1}{r^2}\frac{{\partial }^{2}u}{\partial {\theta }^2}=0;$

u = (c₁ cos αθ + c₂ sin αθ)(c₃r^α + c₄r^−α)