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

Václav Tryhuk; Oldřich Dlouhý

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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 $\bar{x} = ϕ (x),$ $\bar{y} = \bar{y} (\bar{x}) = L (x) y (x) .$ That means, the transformed unknown function $\bar{y}$ 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...