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

2xy''-x(x-1)y'-y=0 about x=0

what are the roots of the indicial equation and for the roots find the recurrence relation that defines the the coef a_{n}

2. Relevant equations

2xy''-x(x-1)y'-y=0 about x=0

assuming the solution has the form y=[itex]\Sigma[/itex]a_{n}x^{n+r}

y'=[itex]\Sigma[/itex](n+r)a_{n}x^{n+r-1}

y''=[itex]\Sigma[/itex](n+r)(n+r-1)a_{n}x^{n+r-2}

3. The attempt at a solution

after plugging into the solution I get

2[itex]\Sigma[/itex](n+r)(n+r-1)a_{n}x^{n+r-1}-[itex]\Sigma[/itex](n+r)a_{n}x^{n+r+1}-[itex]\Sigma[/itex](n+r)a_{n}x^{n+r-1}-[itex]\Sigma[/itex]a_{n}x^{n+r}

then I attempt to make all the x's the same and and make the sigma's equal so after doing that I get

2[itex]\Sigma[/itex](n+r+1)(n+r)a_{n+1}x^{n+r}-[itex]\Sigma[/itex](n+r-1)a_{n-1}x^{n+r}-[itex]\Sigma[/itex](n+r+1)a_{n+1}x^{n+r}-[itex]\Sigma[/itex]a_{n}x^{n+r}

I know that I need to replace the 0 under the sigma's with a (-1) on terms 1,3 but term 2 is whats throwing me off any help would be great

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# Find the series solution,power series

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