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Re: differential equation solve


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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