# Laplace in polar coords

 P: 22 1. The problem statement, all variables and given/known data solve the polar coord equation 2. Relevant equations Urr+(1/r)Ur+(1/r2)U$\vartheta$$\vartheta$=0; 1$\leq$r$\leq$2, 0$\leq$$\vartheta$$\leq$$\pi$/4 U(1,$\vartheta$)=0 U(2,$\vartheta$)=$\vartheta$ U$\vartheta$(r,0)=0 U($\vartheta$,$\pi$/4)=0 and has the form U(r,$\vartheta$)=Uo(r,$\vartheta$)+$\sum$cnRn(r)$\vartheta$n($\vartheta$) 3. The attempt at a solution so I used variation of parameters and the homogeneous boundaries with $\vartheta$ to get $\vartheta$n($\vartheta$)=cos(4n$\vartheta$) then taking r2R''+rR'-cR=0 and using the Euler equation to get r(r-1)+r-c which is r=$\pm$c, c=16n2 so that will give me Rn(r)=Cnr4n+dnr-4n and knowing condition U(1,$\vartheta$)=0 bn=0 so whats left is Cnr4n I got stuck here how do I solve for Cn do I try subbing in conditions to solve or is there some equation im missing and then using the