Re: Quadratic non-linear ODE.
- To: mathgroup at smc.vnet.net
- Subject: [mg37306] Re: [mg37265] Quadratic non-linear ODE.
- From: Selwyn Hollis <selwynh at earthlink.net>
- Date: Tue, 22 Oct 2002 04:48:10 -0400 (EDT)
- References: <200210210629.CAA12261@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Except in some degenerate cases, you're not going to get analytical
solutions. Typically the best you can hope for is an implicit relation
involving y and x. For instance, if you have
dx/dt = f[x,y], dy/dt = g[x,y],
then dy/dx = g[x,y]/f[x,y], and this is "solvable" (in principle) for
the types of equations you describe.
Estudiante Uruguayo 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
> 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.
> Javier Krshpa Sánchez and Héctor Rivera
> http://careers.yahoo.com.au - Yahoo! Careers
> - 1,000's of jobs waiting online for you!
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