A non-elliptic solution of the Lane-Emden equation for index n=5

Abstract

A condition for the existence of non-elliptic solutions of the Lane-Emden equation of index 5 is obtained. It is shown that for a particular non-zero value of the integration constant D the equation admits a non-elliptic solution and thus leads to the modification of the statement of Chandrashekhar [1] that the solution of the Lane-Emden equation of index 5 for non-zero values of D is complicated and involves elliptic integrals. Some characteristics of the new solution curves are also discussed. © 1977.