Solving a nasty rational differential equation

*To*: mathgroup at smc.vnet.net*Subject*: [mg74608] Solving a nasty rational differential equation*From*: Roger Bagula <rlbagula at sbcglobal.net>*Date*: Wed, 28 Mar 2007 01:41:23 -0500 (EST)

I have this nasty differential equation: ( Lorentz invariant elliptical invariant Klein-Gordon) -(hbar2/(2*m))*Sum[D[Phi[x[i]],{x(i),2}],{i,1,4}]+2*m*c2*J{Sqrt[m/m0]]=0 The substition I'm working with is the Kerr mass one of: m/m0->(r/r0)^2 and J as an elliptical invariant like: J[x_]=(-x20+228*x15-494*x10-228*x5-1)3/(1728*x5*(x10+11*x5-1)5) I isolate the radial part of the second differential ( in a polar four sopace the angular part isn't importyant mostly to mass radial solutions) The Phi part is straight forfowd so I'm left with a double interagation of a nasty rational function: ( m^2->r^4) f[x_]=(-x20+228*x15-494*x10-228*x5-1)3/(1728*x*(x10+11*x5-1)5) or if hbar^2/(m^2*c^2)-->r^2 g[x_]=(-x20+228*x15-494*x10-228*x5-1)3/(1728*x^7 *(x10+11*x5-1)5) What I tried after the Integration wouldn't stop in my Mathematica was doing a term wise integration ( 64 terms, every 5th one non-zero).