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Laplace's Equation


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I can solve the following problem by hand using separation of variables:

Given Laplace's equation Uxx+Uyy=0 or D[U,{x,2}]+D[U,{y,2}]==0 in the
column 0<x<L1 and 0<y<L2 satisfying the boundary conditions U(0,y)=0
and U(L1,y)=0. Find U(x,y).

How do I setup and solve this problem automatically using Mathematica? 
DSolve?

Thanks,
Lawrence

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        Lawrence A. Walker Jr., M.Eng./Ph.D. Candidate
                   Morgan State University
          Clarence M. Mitchell School of Engineering
 COMSARE (Center Of Microwave/Satellite And RF Engineering)
           Rm: 306-Schafer     Phone: (443)885-1453
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