Chapter 10.8, Problem 10P

a.

To determine

To show: The Laplace’s equation and the homogeneous boundary conditions determine the fundamental set of solutions $u_0\left(x,y\right)=c_0$, and $u_n\left(x,y\right)=c_n\cosh \left(\frac{n\pi x}{b}\right)\cos \left(\frac{n\pi y}{b}\right),n=1,2,3,\mathrm{...}$

b.

To determine

The function u satisfying the nonhomogeneous boundary condition $u_x\left(a,y\right)=f\left(y\right)$.