Journal of Singularities
volume 10 (2014), 271-285
Received 19 December 2012. Received in revised form 17 August 2013.
An implicit second order ordinary differential equation is said to be completely integrable if there exists at least locally an immersive two-parameter family of geometric solutions on the equation hypersurface like as in the case of explicit equations. An implicit equation may have an immersive one-parameter family of geometric solutions (or, singular solutions) and a geometric solution (or, an isolated singular solution). In this paper, we give a classification of types of completely integrable implicit second order ordinary differential equations and give existence conditions for such families of solutions.
implicit ordinary differential equation, geometric solution, singular solution, complete solution, Clairaut type, reduced type
Mathematical Subject Classification:
Primary 34A26; Secondary 34A09, 34C05, 65L05
Muroran Institute of Technology
Muroran 050-8585, JAPAN