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.

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 ...

... 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 ...

... A PDE is investigated ... can use a Dirichlet boundary condition for the left end of the rod.) (b) Find the temperature of the rod using separation of variables. ...