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Exact solutions of the generalized Lane–Emden equations of the first and second kind

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Abstract

In this paper we discuss the integrability of the generalized Lane–Emden equations of the first and second kinds. We carry out their Noether symmetry classification. Various cases for the arbitrary functions in the equations are obtained for which the equations have Noether point symmetries. First integrals of such cases are obtained and also reduction to quadrature of the corresponding Lane–Emden equations are presented. New cases are found.

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Authors and Affiliations

  1. International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Mmabatho, 2735, Republic of South Africa

    Ben Muatjetjeja & Chaudry Masood Khalique

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  1. Ben Muatjetjeja
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  2. Chaudry Masood Khalique
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Correspondence to Chaudry Masood Khalique.

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Muatjetjeja, B., Khalique, C.M. Exact solutions of the generalized Lane–Emden equations of the first and second kind. Pramana - J Phys 77, 545–554 (2011). https://doi.org/10.1007/s12043-011-0174-4

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