$napis="Abstract"; include "zacatek.inc"; ?> Preprint GA 12/2003
In this paper the necessary and sufficient conditions for a mapping to be the dependence of the complete
solution of some
$\ccj$ first-order ordinary differential equation on the initial Cauchy condition
are deduced. The result is obtained by studying the Cauchy atlas on a manifold
of complete solutions. The proof is constructive - the corresponding differential equation is obtained.
The autonomous case and the linear case are discussed. The relation to the
Sincov functional equation is clarified.
Keywords.
First-order ordinary differential equations, dependence of solutions on the Cauchy conditions,
the Cauchy atlas, maximal flow, local one-parameter group, group of transformations,
the Sincov functional equation.
Mathematics Subject Classification (2000). 34A12, 34C30, 37B55.
include "konec.inc";
?>