Word Count : 108

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Assume a separable solution ( f(x,y,z)=X(x)Y(y)Z(z) ). Then [ \frac{\partial^2 f}{\partial x^2}=X''YZ,\quad \frac{\partial^2 f}{\partial y^2}=XY''Z,\quad \frac{\partial^2 f}{\partial z^2}=XYZ''. ] Substituting into [ \left(\frac{\partial^2}{\partial x^2}+\frac{\partial^2}{\partial y^2}+\frac{\partial^2}{\partial z^2}\right)f+k^2f=0 ] ________ _____ ___ ___ _________ _______ ______ ______ ______ ________.
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