The moving frames for differential equations

I. The change of independent variable



Vaclav Tryhuk, Oldrich Dlouhy

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


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
of the independent variable, the unknown function is preserved.

AMSclassification.  34-02, 34K05, 34A30

Keywords.    Moving coframe, equivalence of differential equations, symmetry of differential equations,
differential invariant, Maurer-Cartan form.