XIV. On the singular solutions of simultaneous ordinary differential equations and the theory of congruencies

Abstract

This paper is an attempt to show how the singular solutions of simultaneous ordinary differential equations are to be found either from a complete primitive or from the differential equations. The latter question has been treated by Mayer (‘Math. Ann.,' vol. 22, p. 368) in a somewhat different way, but with the same result. He also gives a reference to a paper in Polish by Zajaczkowski (summarized in vol.9 of the ‘Jahrbuch der Fortschritte der Mathematik), and to one by Serret in vol. 18 of ‘Liouville’s Journal'.