Solve the boundary-value problem 02 u 0r2 1 r 0u 0r 2 1 r2 u 02 u 0z 2 0, 0 , r , 1, 0

Chapter 14, Problem 17

(choose chapter or problem)

Solve the boundary-value problem

\(\frac{\partial^{2} u}{\partial r^{2}}+\frac{1}{r} \frac{\partial u}{\partial r}-\frac{1}{r^{2}} u+\frac{\partial^{2} u}{\partial z^{2}}=0\),  0<r<1,  0<z<1

u(1, z)=0,  0<z<1

u(r, 0)=0, \(u(r, 1)=r-r^{3}\), 0<r<1

[Hint: See equation (12) in Section 5.3.]

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