       • 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: <a61vil\$gqk\$1@smc.vnet.net>
• 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
>
>             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.

```

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