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Exact solutions of the generalized Lane-Emden equation. (English) Zbl 1009.34002
The main contribution of this article consists of a list of exact solutions to the generalised Lane-Emden equation \(xy''+\alpha y'+\beta x^\nu y^n=0\) for various sets of values for the real parameters \(\alpha\), \(\beta\), \(\nu\) and \(n\). This equation appears in a variety of physical applications, in particular in astrophysics. The authors first derive some fundamental properties of the solutions using equivalence transformations. Then they consider four cases of singular solutions (less than two free parameters) and four cases of general solutions (two-parameter families).

MSC:
34A05 Explicit solutions, first integrals of ordinary differential equations
53D10 Contact manifolds (general theory)
85A04 General questions in astronomy and astrophysics
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