- #1

Mattofix

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## Homework Statement

xu

^{''}+ 2y

^{'}+ xy = 0

## Homework Equations

http://en.wikipedia.org/wiki/Frobenius_method

## The Attempt at a Solution

Ok, so i have managed the Frobenius method in the past, but this seems harder...

[tex]

\sum_{n=0}^{\infty} a_n(n+c)(n+c-1)x^{\ n+c-2} + 2\sum_{n=0}^{\infty} a_n(n+c)x^{\ n+c-2} + \sum_{n=0}^{\infty} a_nx^{\ n+c} = 0

[/tex]

[tex]

\sum_{n=0}^{\infty} a_n(n+c)(n+c-1)x^{\ n+c-2} + 2\sum_{n=0}^{\infty} a_n(n+c)x^{\ n+c-2} + \sum_{n=2}^{\infty} a_{\ n-2}x^{\ n+c-2} = 0

[/tex]

i cannot simply remove n=0 as i would if there were only a difference of one between the sumation limits, here i would have to remove n=0 and n=1 which means that i would not have a quadratic multiplied by [tex]a_0[/tex]to solve, to find the c values. I would have one quadratic multiplied [tex]a_0[/tex] by and one by [tex]a_1[/tex]...