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

... to the PDE to get 2 ODE's. I have included a Wave Equation problem with parts ac, that has variable tension. It involves separation of variables, the Sturm ...

...Separation of Variables. By usingu(x, t) = X(x)T(t) or u(x,y, t) = X(x)Y(y)T(t), separate the following PDEs into two or three ODEs for X and T or X, Y, and ...

... solve the attached Laplace Equation problems using separation of variables. Let := {(x,y) : 0 < x < 1, 0 < y < 1}. (1) Let u(x,y) satisfy the PDE uxx + uyy ...

... 4. By the method of separation of variables and by ... and use it in (2.10): (2.20) And the solution is: (2.21) And the general solution to the PDE (2.1) is the ...

... can write the function as a product of a single-variable functions, namely ... the equation" and the method to achieve this is called "separation of variables". ...

... The general rule for solving such a problems (non-homogenous PDE) is to ... to do that is to apply the Fourier method, that means separation of variables: W ( x ...

... the solution of the heat equation for the temperature in a rod of length L=1 with variable diffusivity: ... We shall use separation of variables by setting: ...

... show the analysis for each situation....I am using separation of variables and Fourier ... write the function as a product of two single-variable functions: (1.7 ...