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 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 0solutions are hard to find. > >Does anybody know whether (analytical) solutions for other values of n >(0grateful if you would give me a hint. > >Very many thanks for your help!! > >Dieter.