1. The problem statement, all variables and given/known data I just have a problem with series solutions when I get to the point of needing to find the recursion relation........and a few other problems. 2. Relevant equations Assume y can be written ∑anxn 3. The attempt at a solution So, on y'' + xy' + 2y = 0, I got to the point of an+2=-an/(n+1). I wrote out a few n's but still can't figure out exactly what the relation is. A little help, maybe? On another problem, (1+x2)y'' - 4xy' + 6y = 0, I got the point of 2a2 + 6a3x - 4a1x + 6a0 + 6a1x + [n=2 to ∞]∑( (n+1)(n+2)an+2 + (n-1)nan - 4nan + 6an)xn = 0. Now what? Detailed help would be much appreciated.