Two-dimensional algebras of dynamic symmetries of ODEs

The efficiency of use of dynamical symmetries at research of integrability of differential equations is shown in this work. The generalization of S. Lie's classification of ordinary differential equations of the second order with respect to twodimensional algebras of point symmetries is constructed. Integrable cases of second order special type ODE are indicated. It is noted that a part of the found integrability cases is related to Abel's type equations and apparently represents independent interest.