Displaying similar documents to “Characterization of several classes of second-order ODEs by using differential invariants.”

The moving frames for differential equations. I. The change of independent variable

Václav Tryhuk, Oldřich Dlouhý (2003)

Archivum Mathematicum

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The article concerns the symmetries of differential equations with short digressions to the underdetermined case and the relevant differential equations with delay. It may be regarded as an introduction into the method of moving frames relieved of the geometrical aspects: the stress is made on the technique of calculations employing only the most fundamental properties of differential forms. The present Part I is devoted to a single ordinary differential equation subjected to the change...

Equivalence and symmetries of first order differential equations

V. Tryhuk (2008)

Czechoslovak Mathematical Journal

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In this article, the equivalence and symmetries of underdetermined differential equations and differential equations with deviations of the first order are considered with respect to the pseudogroup of transformations x ¯ = ϕ ( x ) , y ¯ = y ¯ ( x ¯ ) = L ( x ) y ( x ) . That means, the transformed unknown function y ¯ is obtained by means of the change of the independent variable and subsequent multiplication by a nonvanishing factor. Instead of the common direct calculations, we use some more advanced tools from differential...