On Implicit Second-Order Ordinary Differential Equations: Completely Integrable and Clairaut Type
Authors:
M. Takahashi
Affiliation:
(1) Department of Mathematics, Hokkaido University, Sapporo 060-0810, Japan
Abstract:
In this paper, we give a characterization of implicit second-order ordinary differential equations with smooth complete integrals which we call Clairaut-type equations. Moreover, we consider properties of the Clairaut-type equations and present the duality among special completely integrable equations with respect to Engel–Legendre transformations.