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