## anonymous 4 years ago Solve the differential equation by means of power series about the ordinary point x=0. (1+x^2)y''-4xy'+6y=0

1. anonymous

I'd found the recursion formula to be$a _{m+2}=\frac{-(m-2)(m-3)a _{m}}{(m+2)(m+1)}$ from $y=\sum_{m=0}^{\infty}a _{m}x ^{m}$ using $a _{0},a _{1}$as arbitary holders, my answer for m=2 onwards are 0, ie at m=2, $a _{4}=0$ at m=3, $a _{5}=0$ am i doing the question correctly?

2. experimentX

$a_2 = \frac{-6}{2} a_0 \\ a_3 = -\frac 2 6 a_1 \\ a_4 = ...$ I think at this point it's better to use software to find few terms