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Basically, I have a second-order differential equation for g[y] (given below as odey) and I want to obtain a series solution at $y=\infty$ where g[y] should vanish. That would be easy if the ODE contains polynomial coefficients, hence the Frobenius method can used. But in my case, the coefficients are not polynomial because of the presence of powers proportional to p (can take positive non-integer values). I have also expanded ir at infinity and have taken up to first order (given by irInf) since if I directly use ir, then it would be a mess later for the ODE.

ir[y_] := \[Sqrt](-5 + y^2 + (3 2^(1/3))/(2 + 10 y^2 - y^4 + Sqrt[64 y^2 + 48 y^4 + 12 y^6 + y^8])^(1/3) - (6 2^(1/3)y^2)/(2 + 10 y^2 - y^4 + Sqrt[64 y^2 + 48 y^4 + 12 y^6 + y^8])^(1/3) + (3 (2 + 10 y^2 - y^4 + Sqrt[64 y^2 + 48 y^4 + 12 y^6 + y^8])^(1/3))/2^(1/3))
dir[y_] := D[ir[x], x] /. x -> y
irInf[y_] = Series[ir[y], {y, \[Infinity], 1}] // Normal

p=1/10; (*p>=0*)
odey = (2 irInf[y] - p irInf[y]^(1 - p)) D[irInf[y], y] g'[y] + irInf[y]^2 g''[y] - l (l + 1) g[y] // Simplify

What steps can I take to solve this? Thanks

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