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

Find a general solution in terms of Bessel functions. (Use the indicated transformations and show the details)

2. Relevant equations

[tex]x^2y''+5xy'+(x^2-12)y = 0[/tex]

[tex]y = \frac{u}{x^2}[/tex]

3. The attempt at a solution

I know that the answer needs to be in the form of Bessel functions of the first and second kind, depending on what my roots are.

What is throwing me off is the substitution. The book never explained the nature of substitution for this type of problem. I just literally substituted in that variable like they told me, but I have an inkling that this is extremely wrong, and is going in the completely wrong direction:

[tex]x^2(6ux^{-4})+5x(-2ux^{-3})+(x^2-12)ux^{-2} = 0[/tex]

[tex]-16ux^{-2} + u = 0[/tex]

After this, I reached a dead end. I do not know how to relate this to finding my roots of r from the indicial equation. I have a sense that I need to use the series method first, then somewhere in the middle of the problem, do the substitution.

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# Homework Help: Bessel's Equation

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