LaPlace Equation in Polar

Homework Statement

Solve the Laplace equation: delta u = d2u/dx2+d2u/dy2
inside the half disk 0<r<R, 0<phi<pi
Temperature on the bottom side of the disk is zero, u(x,y=0)=0. Temperature on the upper side of the disk is u(r=R, theta) = u0(phi), 0<phi<pi

Homework Equations

I'm assuming the Laplace equation and the given bc conditions

The Attempt at a Solution

I attempted the solution, which I think up until this point is correct, but I've gotten stuck trying to figure out the constants.

http://img708.imageshack.us/img708/707/p2150074.jpg [Broken]

Thank you all for your help.

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