Re: "Rubbish" integration outputs

*To*: mathgroup at smc.vnet.net*Subject*: [mg45758] Re: "Rubbish" integration outputs*From*: Paul Abbott <paul at physics.uwa.edu.au>*Date*: Fri, 23 Jan 2004 03:15:53 -0500 (EST)*Organization*: The University of Western Australia*References*: <bulomk$8ir$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

In article <bulomk$8ir$1 at smc.vnet.net>, "Iwonder" <yssual at yahoo.com> wrote: > 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? Nothing. > Is Mathematica expected to return such outputs? Yes. Have a look at http://physics.uwa.edu.au/pub/Mathematica/MathGroup/FirstOrderDE.nb 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. Cheers, Paul -- 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 physics.uwa.edu.au AUSTRALIA http://physics.uwa.edu.au/~paul