Chapter 12.5, Problem 6E

In Problems 1–10 solve Laplace’s equation (1) for a rectangular plate subject to the given boundary conditions.

6. $\begin{array}{l}u\left(0,y\right)=g\left(y\right),{\frac{\partial u}{\partial x}|}_{x=1}=0,\\ {\frac{\partial u}{\partial y}|}_{y=0}=0,{\frac{\partial u}{\partial y}|}_{y=\pi }=0\end{array}$