Question

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

Answer 1

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?

Answer 2

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