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

Determine a lower bound for the radius of convergence of series solutions about a) [tex]x_{0}=0[/tex] and b) [tex]x_{0}=2[/tex] for [tex]\left(1+x^{3}\right)y''+4xy'+y=0[/tex].

2. Relevant equations

N/A

3. The attempt at a solution

The zero of [tex]P\left(x\right)=\left(1+x^{2}\right)[/tex] is [tex]-1[/tex]. The distance between [tex]-1[/tex] and [tex]0[/tex] is [tex]1[/tex], so a) [tex]1[/tex]. The distance between [tex]-1[/tex] and [tex]2[/tex] is [tex]3[/tex], so b) [tex]3[/tex].

The only problem is that for b), the back of the book gives [tex]\sqrt{3}[/tex]. What am I doing wrong?

Thanks in advance for your help!

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# Lower bound for radius of convergence of series solutions about a given point

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