/$a(η)[S/η^2 +Fη^2+Gη^4+Hη^6+J]+a'(η) [K/η+ηZ+η^3 C]+a''(η) [η^2 L+P]=0/$
where S,F,G,H,J,K,Z,C,L and P are constants and a(η)
This equation comes from the eigenvalue problem of the graphene nanoring with spin orbit interaction and magnectic field using the mexican-hat potencial. To solve this equation I tried the froebenius method tha didn't work, and the maple software that didn't work too, the group have found a numerical solution using the runge-kunta method, but that's necessary an anathical or semi-analithical solution to compreend the real influence of spin-orbit interaction in graphene.
I would like to add that this is not a homework. In fact, this is an ongoing work with my advisor and after more than one month trying to obtain this solution I decided that I should ask for some help. I appreciate any reference or some hint that could help me with this problem.