 | | From: | Zelah | | Subject: | Lie symmetries for first order ODE via Abel's equation. | | Date: | 11 Nov 2004 18:22:22 -0800 |
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 | In a preprint by Vyacheslav Boyko:
Nonlocal symmetry and Integrable classes of Abel's Equation:
He states "The problem of finding Lie symmetries for the first order
ODE is equivalent to finding solutions to these equations" - (Abel
equations).
Now, how does one reduce finding solutions to
dy/dx = f(x,y)/g(x,y) to
dy/dx = g_3*y^3 + g_2*y^2 + g_1*y^1 + g_0 (Abel's equation second
kind)
Where g_i are functions of x only?
(This should involve lie symmetries!!!)
Also, I have been looking for a preprint:
Integrability of planar polynomial differential systems through linear
differential equations.
I was wondering if anyone knew where to look.
Kind Regards
Zelah
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| | From: | Zelah | | Subject: | Re: Lie symmetries for first order ODE via Abel's equation. | | Date: | 21 Nov 2004 15:48:22 -0800 |
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| cmmahon2001@yahoo.co.uk (Zelah) wrote in message news:...
Hi!
I have found what I have been looking for!
1. One cannot reduce dy/dx = f(x,y) into an Abel equation. I
misunderstood Boyko.
2. I have found Integrability of planar polynomial differential
systems through linear differential equations here:
http://www.udl.es/usuaris/t4088454/ssd/Prepublicaciones/PS/
under
http://www.udl.es/usuaris/t4088454/ssd/Prepublicaciones/PS/liouvil2.ps
Kind Regards
Zelah
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