Lie symmetries for first order ODE via Abel's equation

From: Zelah (cmmahon2001_at_yahoo.co.uk)
Date: 11/14/04


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