The moving frames for differential equations
II. Underdetermined and functional equations

Vaclav Tryhuk, Oldrich Dlouhy

Department of Mathematics, Faculty of Civil Engineering
Brno University of Technology
Veveri 331/95, 662 37 Brno, Czech Republic


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 $y'=f(x,y,z,z')$) 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.

AMSclassification. 34-02, 34K05, 34A30, 34A34, 34K15.

Keywords. Pseudogroup, moving frame, equivalence of differential
equations, differential equations with delay.