From: cmdaven@usit.net
Subject: Re: astronomical Emden or Lane-Emden equation
Date: Mon, 06 Sep 1999 17:03:30 GMT
Newsgroups: sci.math
Keywords: second-order ODE

There is a solution in R. Seshadi and T. Y. Na, "Group Invariances in
Engineering Boundary Value Problems," Springer-Verlag, New York, 1985,
page 193.

Clyde Davenport

Dieter Foertsch <foertsch@ivd.uni-stuttgart.de> wrote:

>Hello,
>
>I have a little problem in finding the (analytical, if it exists)
>solution of the astronomical Emden or Lane-Emden differential equation.
>This DE has the form:
>
>   y"  +  2/x * y'  =  k * y^n
>
>The boundary conditions are: for x=0: y'=0; and for x=1: y=ys.
>
>I know analytical solutions for n=1 and n=0 (these are standard textbook
>solutions). However for other values of n with 0<n<1 analytical
>solutions are hard to find.
>
>Does anybody know whether (analytical) solutions for other values of n
>(0<n<1) exist? Even if only approximative solutions exist I would be
>grateful if you would give me a hint.
>
>Very many thanks for your help!!
>
>Dieter.