(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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

2. Relevant equations

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})

which isn't 0 ?

Perhaps I made the mistake when I differentiated y?

Help would be very much appreciated.

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