Re: DSolve to solve simultaneous ODEs
- To: mathgroup at smc.vnet.net
- Subject: [mg9475] Re: [mg9443] DSolve to solve simultaneous ODEs
- From: Allan Hayes <hay at haystack.demon.co.uk>
- Date: Thu, 6 Nov 1997 02:40:18 -0500
- Sender: owner-wri-mathgroup at wolfram.com
"Kelvin Yip" <ykelvin at unixg.ubc.ca>
[mg9443] DSolve to solve simultaneous ODEs
writes that Mathematica 2.2, even after loading the DSolve package,
cannot solve
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]
x[t]
Kelvin:
I'm afraid that I don't have 2.2 on my machine now, but 3.0 solves the
system:
In[1]:=
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]
Out[1]=
#1 u
E m
{{x -> (------------- & ),
#1 u C[3]
E - E
#1 u C[3]
u C[1] + m n Log[-E + E ]
p -> (-------------------------------- & ),
u
C[3] #1 u
s -> ((-E m u Yp + E u Yp Yx C[2] -
C[3]
E u Yp Yx C[2] -
#1 u #1 u C[3]
E m n Yx Log[-E + E ] +
C[3] #1 u C[3]
E m n Yx Log[-E + E ]) /
#1 u C[3]
((E - E ) u Yp Yx) & )}}
Allan Hayes
hay at haystack.demon.co.uk
http://www.haystack.demon.co.uk/training.html voice:+44 (0)116 2714198
fax: +44 (0)116 2718642
Leicester, UK