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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