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## Homework Statement

∇[itex]^{2}[/itex]u=0 on 0<x<∏, 0<y<2∏

subject to u(0,y)=u(∏,y)=0

and u(x,0)=0, u(x,2∏)=1

## Homework Equations

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## The Attempt at a Solution

I've solved the SLP, and now I am trying to solve the Y-equation that results from separation of variables:

Y''-λY=0, Y(0)=0

Y[itex]_{n}[/itex](y)=Acosh(ny)+Bsinh(ny)

Y(0)=(0)=Acosh(n*0)+Bsinh(n*0)[itex]\Rightarrow[/itex]A=0

Doesn't this effectively "kill" the problem? Or is this the solution:

Y[itex]_{n}[/itex](y)=Bsinh(ny)

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