Word Count : 256

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We start with Laplace's equation in three dimensions: [ \nabla^2 f = \frac{\partial^2 f}{\partial x^2} + \frac{\partial^2 f}{\partial y^2} + \frac{\partial^2 f}{\partial z^2} = 0 ] Assume a solution of the form [ f(x,y,z) = X(x) Y(y) Z(z) ] where (X, Y, Z) are functions of (x, y, z) respectively. Substituting _______ _____ ______ ________ ___ _____ ______ _________ ____ ______ ________.
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