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In this paper, the homoto pyanalysis method
(HAM) is presented to solve some of engineering problems. The homotopy analysis
method is applied in obtaining exact solutions for equations of the type？Δ2=b(x,y) and ？Δ2u=b(x,y,u)？on an elliptical domain. Exact solutions are presented for several
examples involving to demon strate the applic ability and efficiency of HAM.