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

I am attempting to solve the 2nd order ODE as follows using the generalized solution to the Bessel's equation

2. Relevant equations

original ODE:

x[tex]d^{2}y/dx^{2}[/tex]-3[tex]dy/dx[/tex]+xy=0

3. The attempt at a solution

My first thought is to bring out an x^-1 outside of the function so that I end up with:

[tex]x^{-1}([/tex][tex]x^{2}[/tex][tex]d^{2}y/dx^{2}[/tex]-3x[tex]dy/dx[/tex]+[tex]x^{2}[/tex]y)=0

I would then solve the resulting Bessel equation found inside the parentheses, and multiply the resulting solution by x^-1. Is this at all a legal operation? Thank you.

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# Homework Help: Converting 2nd order ODE to Bessel Function

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