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Mathematical Problems in Engineering
Volume 2012, Article ID 614796, 19 pages
Research Article

New Analytic Solution to the Lane-Emden Equation of Index 2

1School of Mathematical Sciences, University of KwaZulu-Natal, Private Bag X01, Pietermaritzburg, Scottsville 3209, South Africa
2Department of Mathematics, University of Venda, Private Bag X5050, Thohoyandou 0950, South Africa

Received 9 November 2011; Revised 11 January 2012; Accepted 13 January 2012

Academic Editor: Anuar Ishak

Copyright © 2012 S. S. Motsa and S. Shateyi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We present two new analytic methods that are used for solving initial value problems that model polytropic and stellar structures in astrophysics and mathematical physics. The applicability, effectiveness, and reliability of the methods are assessed on the Lane-Emden equation which is described by a second-order nonlinear differential equation. The results obtained in this work are also compared with numerical results of Horedt (1986) which are widely used as a benchmark for testing new methods of solution. Good agreement is observed between the present results and the numerical results. Comparison is also made between the proposed new methods and existing analytical methods and it is found that the new methods are more efficient and have several advantages over some of the existing analytical methods.