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## Bessel Function with differential-equations

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Moderator: Shobhit

### Bessel Function with differential-equations

Thu Sep 12, 2013 12:34 pm

Posts: 1
solve $\displaystyle axy''-by'+cxy=0$

step by step

I know the solution is

$\displaystyle y=k_1x^{u}J_{u}\left(\sqrt{\frac{c}{ a}}x\right)+k_2x^{u}Y_{u}\left(\sqrt{\frac{c}{ a}}x\right)$

Where $\displaystyle k_1,k_2$ are arbitrary constant, $\displaystyle a,b,c$ are constant

$\displaystyle u=\frac{a+b}{2a}$

But I don't know how to derive it.