Vyacheslav BOYKO
Institute of Mathematics of NAS of Ukraine,
3 Tereshchenkivs'ka Str.,
01601 Kyiv,
E-mail: boyko@imath.kiev.ua

Symmetry, Equivalence and Integrable Classes of Abel Equations

We suggest an approach for description of integrable cases of the Abel equations. It is based on increasing of the order of equations up to the second one and using equivalence transformations for the corresponding second-order ordinary differential equations. The problem of linearizability of the equations under consideration is discussed.