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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?
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