simplifying first-order diff eq solution

*To*: mathgroup at smc.vnet.net*Subject*: [mg46065] simplifying first-order diff eq solution*From*: "J.S." <childrenoflessergod at yahoo.com>*Date*: Wed, 4 Feb 2004 02:29:35 -0500 (EST)*Organization*: Simon Fraser University*Reply-to*: fugue[at]sfu[dot]ca at sfu.ca*Sender*: owner-wri-mathgroup at wolfram.com

Hi, 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? Please help.