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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.

---
Selwyn Hollis




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
> 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://careers.yahoo.com.au - Yahoo! Careers
> - 1,000's of jobs waiting online for you!
> 
> 

• References:
  • Quadratic non-linear ODE.
    • From: Estudiante Uruguayo <estudfis@yahoo.com.au>