Re: simplifying first-order diff eq solution

*To*: mathgroup at smc.vnet.net*Subject*: [mg46078] Re: simplifying first-order diff eq solution*From*: bobhanlon at aol.com (Bob Hanlon)*Date*: Thu, 5 Feb 2004 04:02:57 -0500 (EST)*References*: <bvq7gc$5ma$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

$Version 4.2 for Mac OS X (August 22, 2002) sol=FullSimplify[ DSolve[{G'[t]==-(s+t) G[t]+1+G[t]^2,G[0]==0},G[t],t][[1]]] {G[t] -> (2*E^((1/2)*(s + t)^2)*s)/ (Sqrt[2*Pi]*s*(Erfi[s/Sqrt[2]] - Erfi[(s + t)/Sqrt[2]]) - 2*E^(s^2/2)) + s + t} However, Version 5.0.1 for Mac OS X fails to solve this. Bob Hanlon In article <bvq7gc$5ma$1 at smc.vnet.net>, "J.S." <childrenoflessergod at yahoo.com> wrote: << I want to solve a first-order simple non-linear differential equation. Incidentally, I even know the solution. Now try to solve this using Mathematica: DSolve[{G'[t] == -( s + t) G[t] + 1 + G[t]^2, G[0] == 0}, G[t], t] You will get a horrible series of Erfi[], while the answer is simply s+t - s Exp[t^2 + st]/(1+s Int_{0}^{t} {dt' Exp[t'^2 / 2 + s t']}) I am sure Mathematica is intelligent enough to reduce the results to this simple form, but how do I do it? For example, why does Mathematica try to express the answer in Erfi[] (instead of erf[]), using complex variables? Can I tell Mathematica that all my variables are real numbers?