Lie symmetries for first order ODE via Abel's equation
From: Zelah (cmmahon2001_at_yahoo.co.uk)
Date: 11/14/04
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Date: 14 Nov 2004 09:56:26 -0800
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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