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**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, u

_{y}(x,1)=-hu(x,1), u(0,y)=u

_{0},

Where h (h>0) and u

_{0}are constants. Derive the expression:

u(x,y)=2hu[itex]_{0}[/itex][itex]\sum[/itex][itex]\frac{1-cos(\alpha_{n})}{\alpha_{n}(h+cos^{2}\alpha_{n})}e^{-\alpha_{n}x}sin(\alpha_{n}y)[/itex]

where [itex]tan\alpha_{n}=\frac{-\alpha_{n}}{h}[/itex] ([itex]\alpha>0[/itex]

## Homework Equations

[itex]u_{xx}+u_{yy}=0[/itex]

[itex] u(x,y)= X(x)Y(y) [/itex]

## 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?

[itex]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}) [/itex]

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