Chapter 10.7, Problem 5E

In Problems 1-5, find a formal solution to the given boundary value problem.

$\begin{array}{rll}\frac{{\partial }^{2}u}{\partial x^2}+\frac{{\partial }^{2}u}{\partial y^2}& =& 0,0<x<\pi ,0<y<1,\\ \frac{\partial u}{\partial x}\left(0,y\right)& =& \frac{\partial u}{\partial x}\left(\pi ,y\right)& =& 0,0\le y\le 1,\\ u\left(x,0\right)& =& \cos x-\cos 3x,0\le x\le \pi ,\\ u\left(x,1\right)& =& \cos 2x,0\le x\le \pi \end{array}$