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MathGroup Archive 2004

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Re: "Rubbish" integration outputs

  • To: mathgroup at smc.vnet.net
  • Subject: [mg45744] Re: "Rubbish" integration outputs
  • From: Roland Franzius <roland.franzius at uos.de>
  • Date: Fri, 23 Jan 2004 03:15:28 -0500 (EST)
  • Organization: Universitaet Hannover
  • References: <bulomk$8ir$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Iwonder wrote:

> Hi,
> 
> 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). So what is
> wrong? Is Mathematica expected to return such outputs?

The result is the general expression for first order linear ODEs.

{{y[x] -> C[2] + Integrate[E^(-2*x - x^2/2 - Log[x])*C[1] +
        (A*E^(-2*x - x^2/2)*Integrate[E^(2*s + s^2/2)/s, {s, 0, x}])/x, x]}}

The innermost dummy variables of the integral in the exponent gets an 
localized  standard name -  DSolve't - for me. The integral cannot be 
solved in this notation because the lower boundary 0 for s produces a 
singularity. You have do to some work by hand here.

-- 

Roland Franzius


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