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Classifications of implicit second-order ordinary differential equations of Clairaut type

Published online by Cambridge University Press:  28 July 2008

Yoshinori Machida  and
Masatomo Takahashi
Yoshinori Machida
Affiliation:
Numazu College of Technology, 3600 Ooka, Numazu-shi, Shizuoka 410-8501, Japan (machida@numazu-ct.ac.jp)
Masatomo Takahashi
Affiliation:
Mathematical Science, Common Subject Division, Muroran Institute of Technology, Muroran 050-8585, Japan (masatomo@mmm.muroran-it.ac.jp)
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Abstract

We study an implicit second-order ordinary differential equation with complete integral. The class of second-order Clairaut-type equations is an important class of completely integrable equations. Indeed, the notion of second-order Clairaut-type equations is the generalization of second-order classical Clairaut equations. We give generic classifications of second-order Clairaut-type equations under the weak equivalence and the one-parameter strict equivalence relations.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 138 , Issue 4 , August 2008 , pp. 821 - 842
Copyright
2008 Royal Society of Edinburgh

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