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

Solve

[tex](1-4x^2)y''+34x\cdot y'-70y=0[/tex]

2. Relevant equations

Basically, I found the recurrence relationship to be:

[tex] a_{n+2}=\frac{2 (-7 + n) (-5 + 2 n)}{(n+1)(n+2)}a_n}[/tex]

Now, I solve for y1 where y1 had a_0=0 and a_1 = 1. It is a simple polynomial of degree 7.

That was the first part.

The second part wants me to find the radius of convergence of y2, where y2 has a_0=1 and a_1 = 0.

In this case, all the odd coefficients are equal to 0. But I am having a hard time trying to find the radius of convergence. I actually don't have a clue here.

I tried doing the ratio test directly on the recurrence term, but led me to 1/x^2, but that didn't work, and I think I did wrong to.

I tried finding the pattern and trying to find what the series actually was, but couldn't. :S

So, now I'm stuck.

(P.S. For the patternn, I got a_n = [tex] \frac{2*(-7)(-5)(..)(2n-9)(-5)(-1)(3)(7)(4n-9)}{(2n)!}[/tex]

But it appears to be invalid when I do the ratio test on it according to webworks.

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# ODE - Power Series Convergence

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