Geodesic
The moving frames for differential equations. II. Underdetermined and functional equations
Archivum mathematicum, Tome 40 (2004) no. 1, pp. 69-88.

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Continuing the idea of Part I, we deal with more involved pseudogroup of transformations $\bar{x}=\varphi (x)$, $\bar{y}=L(x)y$, $\bar{z}=M(x)z,\, \ldots $ applied to the first order differential equations including the underdetermined case (i.e. the Monge equation $y^{\prime }=f(x,y,z,z^{\prime })$) and certain differential equations with deviation (if $z=y(\xi (x))$ is substituted). Our aim is to determine complete families of invariants resolving the equivalence problem and to clarify the largest possible symmetries. Together with Part I, this article may be regarded as an introduction into the method of moving frames adapted to the theory of differential and functional-differential equations.
Classification : 34A25, 34A26, 34C14, 34C41, 34K05, 34K17, 53B21
Keywords: pseudogroup; moving frame; equivalence of differential equations; differential equations with delay 
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Tryhuk, Václav; Dlouhý, Oldřich. The moving frames for differential equations. II. Underdetermined and functional equations. Archivum mathematicum, Tome 40 (2004) no. 1, pp. 69-88. http://geodesic.mathdoc.fr/item/ARM_2004__40_1_a7/