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Re: Solving a nasty rational differential equation

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  • Subject: [mg74625] Re: Solving a nasty rational differential equation
  • From: dh <dh at>
  • Date: Thu, 29 Mar 2007 02:25:57 -0500 (EST)
  • References: <eud32p$k50$>

$Version=5.1 for Microsoft Windows (October 25, 2004)

Ho Roger,

if you want a clear cut answer, then do not give details that are 

irrelevant and can not be understood without context , but concentrate 

on the question. I can only guess what your problem is. Do you want to 

integrate g[x] twice, like Integrate[Integrate[g[x],x],x]? What does 

x20, x15 e.t.c. mean, are these constants or should it read x^20 ...? 

Anyway in both cases Mathematica will integrate without problems.


Roger Bagula wrote:

> 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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