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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 '' +αy ' +βx ν y n =0 for various sets of values for the real parameters α, β, ν 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:
34A05Methods of solution of ODE
53D10Contact manifolds, general
85A04General topics of astronomy and astrophysics