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Δu(r,θ)=0, 1 ≤ r ≤ 2, 0 ≤ θ ≤ pi

and here are the Boundary Conditions:

u(1,θ)=sin(θ), u(2,θ)=0, u(r,0)=0, u(r,pi)=0

Based on the Boundary Conditions I believe this is half of an annulus.

Using the 2D Laplace equation for polar coordinates, find the solution u(r,θ).

I've begun to separate variables, R(r) and Theta(θ), but I'm confused with whether I should use as +,-, or 0. The steps after that I am stuck on as well. Also, what kind of Laplace equation is this (Dirichlet, Neumann, etc.)?

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# Laplace Differential Equation of a Half-Annulus

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