I need help in a bonus problem

1. May 19, 2008

momen salah

hi guys it's me you helped me last time in my bonus problem(thank's for that) i need help again naw please it's a two marks bonus problem:

solve using power series:
(x^2)(y")+y=0

after solving it i stoped at :

an[n^2-n+1]=0

2. May 21, 2008

HallsofIvy

Try a solution of the form
$$y= \sum_{n=0}^{\infty} a_nx^{n+i}$$

where i is not necessarily positive nor even an integer. Look at the lowest powers after you have put that into the differential equation (and assume a0 is NOT 0) in order to determine i.