Re: How solve a system of ODE with periodic coeffs.
- To: mathgroup at smc.vnet.net
- Subject: [mg30721] Re: How solve a system of ODE with periodic coeffs.
- From: "W. H. Harker" <wharke at sprynet.com>
- Date: Sat, 8 Sep 2001 02:56:00 -0400 (EDT)
- References: <9nal83$np0$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
In article <9nal83$np0$1 at smc.vnet.net>, guillerm at aida.usal.es says...
> I would like solved System of ODE with periodic coeffs. as this:
>
> DSolve[{Derivative[1][x1][t] == Cos[t]*x1[t] + 1.5*x2[t],
> Derivative[1][x2][t] == 2.1*x1[t] + 2.3*x2[t], x1[0] == 1, x2[0] ==
> 0}, {x1[t], x2[t]}, t]
>
> I wish obtain the analitycal solution. I have tested with DSolve but
> doesn`t work (Even using Rationalize, giving numeric values of initial
> conditions,i.e.: a =1).
This is Hill's equation (it's close to a Mathieu equation but a little
more complicated). It can have exponentially growing oscillatory
solutions, quasiperiodic solutions and, a small subset, periodic
solutions. Unless you are extremely lucky there are no closed form
solutions to this ODE. Use NDSolve.
Reference: "Hill's Equation"
W. Magnus & S. Winkler
Interscience 1966
Hope this is of some help
Wes Harker