Hi, I'm stuck on this question from a calculus book;(adsbygoogle = window.adsbygoogle || []).push({});

Show that y'' + ((1+2n)/x)y' + y = 0 is satisfied by x^{-n}J_{n}(x)

Is it correct that when I differentiate that, I get these:

y= x^{-n}J_{n}(x)

y'=-x^{-n}J_{n+1}(x)

y''=nx^{-n-1}J_{n+1}(x) -

x^{-n}(dJ_{n+1}(x)/dx)?

3. The attempt at a solution

Equation in question becomes:

x^{-n}(2(n/x)J_{n+1}- J_{n}- ((1+2n)/x)J_{n+1}+ J_{n})

= x^{-n}(-x^{-1}J_{n+1})

but this isn't 0.

Sorry if I'm repeating myself here but I could just do with some kind of a pointer.

Thanks, Kris

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# Homework Help: Showing that a bessel function satisfies a particular equation

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