I ended up with a differential equation that looks like this: $$\frac{d^2y}{dx^2} + \frac 1 x \frac{dy}{dx} - \frac{ay}{x^2} + \left(b -\frac c x - e x \right )y = 0.$$ I tried with Mathematica. But could not get the sensible answer. May you help me out how to solve it or give me some references that I can go over please? Thanks.
Special Differential Equation
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ordinary-differential-equations
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0What is the domain of your problem? – 2012-10-14
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0Basically it is a radial component of the Schrodinger equation in Cylindrical co-ordinates. For this reason the domain has to be x>0. – 2012-10-16