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There is a function V(x,y,z) such that:

[tex]\nabla^2 V = \delta(x)\delta(y)\delta(z) \frac{q}{\epsilon_0} [/tex]

with boundary conditions at infinity V=0.

Since there is spherical symmetry, I was able to rewrite it just in terms of the radial distance, and got:

[tex]\nabla^2 V = \frac{q}{\epsilon_0 r} = \frac{q}{\epsilon_0 \sqrt{x^2 + y^2+z^2}}[/tex]

But now I'm dealing with a system with an extra term:

[tex]\nabla^2 V = \delta(x)\delta(y)\delta(z) \frac{q}{\epsilon_0} - (\partial_x V) \frac{a}{1+ax}[/tex]

a is a constant, and the boundary condition is that V->0 when y or z go to infinity.

I am very rusty with differential equations. Can someone tell me how to attack this?

Also, is this still considered linear since there is no term with just V in it? If I knew what to call this class of equations, maybe I could find some solutions in a table or something.