Thanks guys ... I had started on the "divide one equation by the other" path, but for some reason did not carry it to it's conclusion.
@HallsofIvy, the first equation actually does depend on l; I guess you mistook the l in the numerator for 1. Thanks anyway :)
I have the equations
\frac{l}{u^{2}} \frac{du}{dx}=constant
and
\frac{1}{u} \frac{dl}{dx}=constant.
By "eyeball", I can say the solution is
l \propto x^{n} \ and \ u \propto x^{n-1}.
I can't see how I could arrive at these solutions 'properly', if you know what I mean
In the x-y plane, we have the equation
\nabla^{2} \Psi = - 4\pi \delta(x- x_{0}) \delta (y- y_{0})
with \Psi = 0 at the rectangular boundaries, of size L.
A paper I'm looking at says that for
R^{2} = (x-x_{0})^{2} + (y-y_{0})^{2} << L^{2} ,
that is, for points...