On the point transformations for the equation $y''= P + 3Qy' + 3R{y'}^2 + S{y'}^3$

Abstract

For the equations $y''=P(x,y) + 3Q(x,y)y' + 3R(x,y){y'}^2 + S(x,y){y'}^3$ the problem of equivalence is considered. Some classical results are resumed in order to prepare the background for the study of special subclass of such equations, which arises in the theory of dynamical systems admitting the normal shift.