An algebraic approach to a study of two-dimensional affine differential system.

In a present paper a problem of classification of Aff(2;R)orbits’ dimensions is considered on example of an autonomous two-dimensional ane dierential system of first order. Methods of Lie algebras are used in the work, as well as methods of group analysis. Computer algebra systems ”Bergman” and ”Mathematica 5.0” are widely used. Mathematics Subject Classification 2000: 34C14, 34C05, 58F14.