THE STUDY OF SOME CHARACTERISTICS OF THE SOLUTIONS OF THE ABEL EQUATION OF THE SECOND KIND

Abstract

In this paper, we study the Abel differential equation of the second kind

\[
y'=\frac{f_2(x)y^2+f_1(x)y+f_0(x)}{y+g(x)}.
\]

Treating different assumptions for the functions \(f_2(x)\), \(f_1(x)\), \(f_0(x)\) and \(g(x)\), we prove five theorems dealing with the qualitative features of the solutions of the above mentioned equation.