Solve Power Series: (x^2)(y") + y = 0

[momen salah]

Homework Statement

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

Homework Equations

The Attempt at a Solution

after solving it i stopped at :

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

 

[Dick]

Your problems are coming from the fact that the differential equation is singular at 0. You can't expand it in a power series around x=0. You'll have to expand around another point if you want to do it that way. For example let u=x+1. Then the equation becomes (u-1)^2*y''+y=0. Now expand it as a series in u.