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MathGroup Archive 2004

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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.


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