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