# PDE Harmonic Function help

PDE Harmonic Function help!!

## Homework Statement

A bounded harmonic function u(x,y) in a semi-infinite strip x>0, 0<y<1 is to satisfy the boudary conditions:
u(x,0)=0, uy(x,1)=-hu(x,1), u(0,y)=u0,
Where h (h>0) and u0 are constants. Derive the expression:
u(x,y)=2hu$_{0}$$\sum$$\frac{1-cos(\alpha_{n})}{\alpha_{n}(h+cos^{2}\alpha_{n})}e^{-\alpha_{n}x}sin(\alpha_{n}y)$

where $tan\alpha_{n}=\frac{-\alpha_{n}}{h}$ ($\alpha>0$

## Homework Equations

$u_{xx}+u_{yy}=0$

$u(x,y)= X(x)Y(y)$

## The Attempt at a Solution

I Cant seem to even come close to the answer.
Maybe some hints as to how i should approach this?
$Y(y)=C(e^{\alpha_{n}y}-e^{-\alpha_{n}y}), Y(0)=0, X(x)=C_{1}cos(\alpha_{n}x)+C_{2}sin(\alpha_{n}x), \frac{-\alpha_{n}}{h}=tanh(\alpha_{n})$

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