**1. Introduction**

Given a scalar ordinary differential equation in normal form, say

$$y' = \omega(\mathfrak{x}, y),\tag{1}$$

where we assume the usual existence and uniqueness conditions, i.e., *<sup>ω</sup>* : <sup>Ω</sup> <sup>⊂</sup> <sup>R</sup><sup>2</sup> <sup>→</sup> <sup>R</sup> is a Lipschitz-continuous function and Ω is an open set, it is well known that the problem of representing its solutions in terms of elementary, or special, functions is, in general, analytically intractable. In some well known and particular situations, this representation is possible, according to some specific structure of the equation itself. Among the elementary solution methods, the most advanced is that of the search for an integrating factor, which, as we know, is related to the determination of a Lie symmetry, see [1] Section 2.5. When the integrating factor depends on both variables (*x*, *y*) some old-school texbooks like, for instance, [2] pages 50–51 or [3] pages 53–55, seek for the integrating factor using an "inspection method", useful when the given equation presents a particular structure. This special technique has a long, and probably forgotten, history. It was, in fact, introduced by the Italian mathematician Jacopo Francesco Riccati (1676–1754) and was published posthumously in 1761, in the first [4] of four tomes of Riccati, Opera Omnia, dedicated to his lectures on differential equations. Riccati called his method "dimidiata separazione" which can be translated as splitted separation. This paper is devoted to one particular family of equations studied by Riccati, revisiting it in terms of Lie symmetry and using the 2F1 Gauss hypegeometric function to express in closed form its integral curves. Moreover, using Lie symmetry we solve a more general equation of the same kind.
