Explain detailed explanation to separation of variables

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Reference no: EM13123181

Detailed Explanation to Separation of variables

Hello. I am having some trouble with the following PDE:

Laplacian(u(x,y,z)) = u(x,y,z) * (-2*E/h^2)*(1 + (GM/(2(x^2+y^2+z^2)^(1/2))))^4

Where, G,M,E, and h are all constants.

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.

Reference no: EM13123181

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