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MathGroup Archive 2004

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Re: "Rubbish" integration outputs

  • To: mathgroup at
  • Subject: [mg45758] Re: "Rubbish" integration outputs
  • From: Paul Abbott <paul at>
  • Date: Fri, 23 Jan 2004 03:15:53 -0500 (EST)
  • Organization: The University of Western Australia
  • References: <bulomk$8ir$>
  • Sender: owner-wri-mathgroup at

In article <bulomk$8ir$1 at>, "Iwonder" <yssual at> 

> I always find me in troubles when integrating ODE that I think Mathematica
> should be able to do. It's all right for the very simplest, but consider for
> instance the following:
> \!\(DSolve[\((x + 2  x\^2 + x\^3)\) \(y'\)[x] + \(x\^2\) \(y''\)[x] == A, y,
>     x]\)
> 'A' a constant. Well, the problem is that I don't even the clue that
> Mathematica *cannot* integrate it, there is some output with gibberish, like
> K$14646 and the like (those are intermediary variables I guess). 

If you look up the online documentation for DSolve and scroll down to 
the Further Examples section it says that 

  K$ variables are used as dummy integration variables.

> So what is wrong? 


> Is Mathematica expected to return such outputs?


Have a look at

for a first-principles analysis of your ODE. 

By series expansion it is straightforward to show that the solution to 
your ODE is not analytic at x == 0.


Paul Abbott                                   Phone: +61 8 9380 2734
School of Physics, M013                         Fax: +61 8 9380 1014
The University of Western Australia      (CRICOS Provider No 00126G)         
35 Stirling Highway
Crawley WA 6009                      mailto:paul at 

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