       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).

```

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