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I am looking for the general solution the the following equation:

$\frac{d}{dx}(x^n du/dx) + x^nu=o$, $n=1,2,3,.....$

I changed it to $\frac{d^2u}{dx^2}$ + $\frac{n}{x} \frac{du}{dx} + u = 0$

I think it is supposed to become a bessel equation, but the format doesn't quite look like one.

I am not sure how to proceed.

Please help!

Vidyanshu Mishra
  • 10,143
David House
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  • Actually this is a Sturm-Lioville equation $$\frac{\text{d}}{\text{d}x} \left(p(x) \frac{\text{d}u}{\text{d}x} \right) + q(x) u = -\lambda w(x) u$$ with $p(x)=w(x)=x^n$ and $q(x)=0$. See here https://en.wikipedia.org/wiki/Sturm-Liouville_theory. There is a lot of solution theory for this type of equations. You can look into this. – Cahn Dec 03 '16 at 15:47
  • I will look at it that way to start – David House Dec 03 '16 at 16:06

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