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On the contact equivalence problem of second order ODEs which are quadratic with respect to the second order derivative

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Abstract

In the present paper we establish the necessary and sufficient conditions for two ordinary differential equations of the form y″2 + A(x, y, y′)y″ + B(x, y, y′) = 0 to be equivalent under the action of the pseudogroup of contact transformations. These conditions are formulated in terms of integrals of some one-dimensional distributions.

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Authors and Affiliations

  1. Kazan Federal University, Kazan, Russia

    Vadim V. Shurygin Jr.

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  1. Vadim V. Shurygin Jr.
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Correspondence to Vadim V. Shurygin Jr..

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(Submitted by M. A. Malakhaltsev)

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Shurygin, V.V. On the contact equivalence problem of second order ODEs which are quadratic with respect to the second order derivative. Lobachevskii J Math 34, 264–271 (2013). https://doi.org/10.1134/S1995080213030098

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  • DOI: https://doi.org/10.1134/S1995080213030098

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