On the integral curve of a linear third order O. D. E (Q1355842)

The integral curves \(\gamma\) of the third-order linear differential equation \[ y'''+ 3p_1y''+ 3p_2y'+ p_3y= 0\tag{\(*\)} \] with smooth variable coefficients \(p_j\) is studied. Here, \(\gamma: \mathbb{R}\to \mathbb{R}\mathbb{P}^2\) is defined in homogeneous coordinates by \([y_1: y_2: y_3]\), where \(y_1\), \(y_2\), \(y_3\) are linearly independent solutions to \((*)\). A similar approach to the above-mentioned matter is used in the monography [\textit{F. Neuman}, Global properties of linear ordinary differential equations, Academia Praha and Dodrecht: Kluwer Academic Publishers (1991; Zbl 0784.34009)] and in papers, mentioned there. This fact is not mentioned by the author.