The problem that I'm having is that there is a nonconstant factor of (x^2+y^2+z^2)^(-1/2) appearing on the RHS of this equation, making it non-trivial to solve. I tried separation of variables, and couldn't seem to get it to work.

Could someone please take a look?
Thanks!

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This equation does not separate in rectangular coordinates, so you need to convert to spherical coordinates. In these coordinates, the equation becomes

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