Re: Quadratic non-linear ODE.
- To: mathgroup at smc.vnet.net
- Subject: [mg33180] Re: Quadratic non-linear ODE.
- From: sri <srikumar at umich.edu>
- Date: Wed, 6 Mar 2002 01:56:42 -0500 (EST)
- Organization: University of Michigan Engineering
- References: <firstname.lastname@example.org>
- Sender: owner-wri-mathgroup at wolfram.com
Try laplace transforms. You will have to express them in terms of convolutions though. based on the equations i derive the following: cx^2=ax^2+bx^2 which means c=a+b; (assuming x is a continuos function) from there im not too sure. ill take a look at it later Javier wrote: > Hi, how are you? We are almost graduated physics > students from south america. Due to our final work, > certain coupled non-linear ODE systems have appear, > and we don't have any idea about how to resolve it, in > spite we attempt to. For our purposes, we would need > analytical solutions -if there exist- for the > following systems, > > dx/dt = ax^2 + by^2 > > dx/dt = cx^2 > > dx/dt = axy + by^2 > dy/dt = cxy + dx^2 > > Where a, b, c and d are known constants paremeters of > the problem. We would be very grateful if you can help > us with this matter. We were able to fit numerically > the solutions for both systems, in a relatively wide > range of values, but we did not find anything aboout > the analytical solutions for none of the systems. In > brief words, for our work we would need the explicit > expressions for x(t) and y(t), if they are known, of > course. If you can help us, please contact us at, > > estudfis at yahoo.com.au > > We are very grateful, since this moment. > Sincerely, > > Javier Krshpa Sánchez and Héctor Rivera Firpo > > Montevideo, Uruguay. > > http://movies.yahoo.com.au - Yahoo! Movies > - Vote for your nominees in our online Oscars pool.