Effective procedure of point-classification for the equation $y'' = P + 3 Q y' + 3 R {y'}^2 + S {y'}^3$

Abstract

For the equations of the form $y''=P(x,y)+3 Q(x,y) y'+3 R(x,y) {y'}^2 +S(x,y) {y'}^3$ the problem of equivalence in the class of point transformations is considered. Effective procedure for determining the class of point equivalence for the given equation is suggested. This procedure is based on explicit formulas for the invariants.