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MathGroup Archive 2006

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Re: differential equation solve

  • To: mathgroup at smc.vnet.net
  • Subject: [mg68841] Re: differential equation solve
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
  • Date: Mon, 21 Aug 2006 03:27:37 -0400 (EDT)
  • Organization: The Open University, Milton Keynes, UK
  • References: <ec97f9$4bn$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

elvis wrote:
> another equation:
> 
> \!\(DSolve[{\(x'\)[t] == r*x[t] \((1 - x[t]\/xm)\), x[0] == x0}, x,
> t]\)
> 
> this face anothe prolbem

Assuming that the "problem" you faced is the *warning* message returned 
by DSolve, you can easily check that the returned solution is correct:

sol = DSolve[{Derivative[1][x][t] == r*x[t]*(1 - x[t]/xm), x[0] == x0}, 
x, t]

--> Solve::"ifun" : "Inverse functions are being used by (Solve), so 
some solutions may not be found; use Reduce for complete solution 
information.

--> {{x -> Function[{t}, E^(r*t)*x0*(xm/(-x0 + E^(r*t)*x0 + xm))]}}

Simplify[{Derivative[1][x][t] == r*x[t]*(1 - x[t]/xm), x[0] == x0} /. 
sol[[1]]]

--> {True, True}

HTH,
Jean-Marc


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