Re: DSolve to solve simultaneous ODEs
- To: mathgroup at smc.vnet.net
- Subject: [mg9467] Re: DSolve to solve simultaneous ODEs
- From: Bill Bertram <wkb at ansto.gov.au>
- Date: Thu, 6 Nov 1997 02:40:11 -0500
- Organization: ANSTO
- Sender: owner-wri-mathgroup at wolfram.com
Kelvin Yip wrote:
>
> Hi Everyone,
>
> Although I follow closely the Mathematica book's instruction , I still
> only receive a out put which is just a parapharse of my input. The
> Program (Version 2.2) work well on solving single equation but not a
> systems of ODEs, anyone can help ?
Kelvin,
I haven't tried this using Version 2.2 but Mathematica Version 3.0
solves this set of simultaneous equation without any trouble!
DSolve[{(u*x[t]*(1-x[t]/m)-x'[t]==0),
(n*x[t]-p'[t]==0),(-p'[t]/Yp-x'[t]/Yx-s'[t]==0)},{x,p,s},t]
maybe you should upgrade.
Cheers,
Bill
By the way, the solution given by Mathematica V3.0 is,
{x[t] -> (Exp[t*u]*m)/(Exp[t*u] - Exp[C[3]]),
p[t] -> (u*C[1] + m*n*Log[-Exp[t*u] + Exp[C[3]]])/u,
s[t] -> 1/((Exp[t*u] - Exp[C[3]])*u*yp*yx)*
(-Exp[C[3]]*m*u*yp + Exp[t*u]*u*yx*C[2]*yp -
Exp[C[3]]*u*yx*C[2]*yp -
Exp[t*u]*m*n*yx*Log[-Exp[t*u] + Exp[C[3]]] +
Exp[C[3]]*m*n*yx*Log[-Exp[t*u] + Exp[C[3]]])}