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