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>