Оn the right and inverse problems of group analysis of the autonomous systems of ordinary second-order differential equations
The solvability of the right and inverse problem of group analysis for some systems of two ordinary second-order differential equations is discussed. Large classes of such systems that allow a Lie group operators have been found. It has been proved that the studies of such systems are reduced to studies of the systems of two ordinary first-order differential equations, where the first equation is the Abel 2nd kind equation and it is solved independently of the second equation of the system.