- #1

dp182

- 22

- 0

## Homework Statement

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}

## Homework 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}

## 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 what's throwing me off any help would be great