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    Coupled differential equations

    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 :)
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    Coupled differential equations

    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
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    2-D Poisson's equation - Green's function

    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...