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Re: differential equation solve
*To*: mathgroup at smc.vnet.net
*Subject*: [mg68851] Re: differential equation solve
*From*: Peter Pein <petsie at dordos.net>
*Date*: Mon, 21 Aug 2006 03:28:02 -0400 (EDT)
*References*: <ec97f9$4bn$1@smc.vnet.net>
*Sender*: owner-wri-mathgroup at wolfram.com
elvis schrieb:
> Here we often use mathematica to solve differential equations, when I
> encouter a equation with several constrains I set them to those values.
> But it cannot solve it and have the following warnings:
>
> DSolve::deqx: Supplied equations are not differential equations of
> the given functions.
>
> Give a very simple differential equation here:
>
> DSolve[{y'[x] == r*y[x], y[0] == a}, y, x]
>
> another equation:
>
> \!\(DSolve[{\(x'\)[t] == r*x[t] \((1 - x[t]\/xm)\), x[0] == x0}, x,
> t]\)
>
> this face anothe prolbem
>
> Can anyone help to "solve" this problem for me?
> Thanks!
>
Do you use Mathematica 0.1 alpha?
Even this one solves these equations:
$Version
"4.0 for Microsoft Windows (July 16, 1999)"
DSolve[{Derivative[1][y][x] ==
r*y[x], y[0] == a}, y, x]
{{y -> (a*E^(r*#1) & )}}
DSolve[{Derivative[1][x][t] ==
r*x[t]*(1 - x[t]/xm),
x[0] == x0}, x, t]
{{x -> ((E^(r*#1)*x0*xm)/(-x0 + E^(r*#1)*x0 +
xm) & )}}
and so does 5.1 for Windows:
{{y -> Function[{x}, a*E^(r*x)]}}
{{x -> Function[{t}, (E^(r*t)*x0*xm)/
(-x0 + E^(r*t)*x0 + xm)]}}
Peter
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