The general solution of the Laplace's equation in the Cartesian system can be written as h(x,y)...

   

  

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The general solution of the Laplace's equation in the Cartesian system can be written as h(x,y) = X(x)Y(y) with X(x) = A cosh (1x) + B sinh (Ax), Y(y) = C cos (Ay) + D sin (Ay), by assuming the homogenous boundary conditions are in the Y direction. In the polar coordinate system, the Laplace's equation is u 1 du 1 0u + r r r r 20 The general solution is + h(x, y) = (0)R(r), 0. The general solution of the Laplace's equation in the Cartesian system can be written as h(x,y) = X(x)Y(y) with X(x) = A cosh (1x) + B sinh (Ax), Y(y) = C cos (Ay) + D sin (Ay), by assuming the homogenous boundary conditions are in the Y direction. In the polar coordinate system, the Laplace's equation is u 1 du 1 0u + r r r r 20 The general solution is + h(x, y) = (0)R(r), 0.

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