Valery A.Yumaguzhin,

Differential invariants of 2-order ODEs, I. 

In this paper, we investigate the action of pseudogroup of all point transformations 
on the natural bundle of equations
$$
  y''=a^3(x,y)y'\,^3+a^2(x,y)y'\,^2+a^1(x,y)y'+a^0(x,y)
$$
We construct differential invariants of this action and solve the equivalence problem 
for some classes of these equations in particular for generic equations.