Find a solution to the mixed boundary value problem

Chapter 10, Problem 17E

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Find a solution to the mixed boundary value problem

 \(\frac{\partial^{2} u}{\partial r^{2}}+\frac{1}{r} \frac{\partial u}{\partial r}+\frac{1}{r^{2}} \frac{\partial^{2} u}{\partial \theta^{2}}=0\)

\(\(1<r<3, \quad-\pi \leq \theta \leq \pi\)

\(u(1, \theta)=f(\theta),-\pi \leq \theta \leq \pi\)\)

\(\frac{\partial u}{\partial r}(3, \theta)=g(\theta), \quad-\pi \leq \theta \leq \pi\)

Equation Transcription:

Text Transcription:

\partial^2 u \partial r^2+1 r\partial u\partial r+1r^2 \partial^2 u\partial \theta^2=0

1<r<3, \quad-\pi \leq \theta \leq \pi

u(1, \theta)=f(\theta),-\pi \leq \theta \leq \pi

\partial u\partial r 3, \theta)=g(\theta), \quad-\pi \leq \theta \leq \pi

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