Question

Find the general solution in terms of a polynomial and a series in powers of x+1:

x(2+x)y'' + (2+x)y' + 2y = 0

Answer 1

After using

\[y(x) = \sum_{m=0}^{\infty}a_{m}(x+1)^{n}\]

I've found a formula for the constants:

\[a_{m+2} = \frac{ a_{m+1}(m+1)+a_{m}(m^{2}+2) }{ (m+2)(m+1) }\]

But I'm not sure where to go from here.