  In this paper we revisit the relationship between the Einstein--Friedman and
the Abel equations to demonstrate how it might be applied to the inflationary
analysis in a flat Friedman universe filled with a real-valued scalar field.
The analysis is performed for three distinct cases of polynomial potentials. As
a result of a numeric integration of Abel equation, the necessary and
sufficient conditions for both slow-rolling and inflation proper are estimated
with respect to the initial value of the field. In addition, the relationship
between the slow-rolling condition and the inflation is ascertained.
