Re: simplifying first-order diff eq solution

*To*: mathgroup at smc.vnet.net*Subject*: [mg46134] Re: simplifying first-order diff eq solution*From*: ghrabovsky at tds.net (George Hrabovsky)*Date*: Sat, 7 Feb 2004 04:02:27 -0500 (EST)*References*: <bvq7gc$5ma$1@smc.vnet.net> <bvt1lo$oln$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

I go this result with: DSolve[{G'[t] == -( s + t) G[t] + 1 + G[t]^2, G[0] == 0}, G[t], t] // FullSimplify Out[203]= 2 1/2 (s + t) {{G[t] -> s + t + (2 E s)/ 2 s /2 (-2 E + Sqrt[2 Pi] s s s + t (Erfi[-------] - Erfi[-------]))}} Sqrt[2] Sqrt[2] bobhanlon at aol.com (Bob Hanlon) wrote in message news:<bvt1lo$oln$1 at smc.vnet.net>... > $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?