Department of Mathematics, Faculty of Civil Engineering
Brno University of Technology
Veveri 331/95, 662 37 Brno, Czech Republic
E-mail. email@example.com firstname.lastname@example.org
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.