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On completely integrable implicit ordinary differential equations

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Please use this identifier to cite or link to this item:http://doi.org/10.14943/84111

Title: On completely integrable implicit ordinary differential equations
Authors: Takahashi, Masatomo Browse this author
Keywords: implicit ordinary differential equation
geometric solution
singular solution
complete solution
Clairaut type
reduced type
Issue Date: 23-Jul-2010
Journal Title: Hokkaido University Preprint Series in Mathematics
Volume: 964
Start Page: 1
End Page: 20
Abstract: For smooth explicit n-th order ordinary differential equations, there exists a unique solution with initial condition and hence exists an n-parameter family of solutions at least locally. On the other hand, for smooth implicit ordinary differential equations, existence and uniqueness for solutions with initial condition does not hold. In this paper, we give a necessary and sufficient condition for existence of an n-parameter family of geometric solutions in the smooth category. Moreover, we give a sufficient condition that implicit ordinary differential equations have a unique geometric solution with initial condition. As a consequence, we classify completely integrable first and second ordinary differential equations in detail.
Type: bulletin (article)
URI: http://hdl.handle.net/2115/69771
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics

Submitter: 数学紀要登録作業用

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