On the obstruction to linearizability of second-order ordinary differential equations

In this paper, we investigate the action of the pseudogroup of all point transformations on the bundle of equations y" = u(0)(x, y) + u(1)(x, y) y' + u(2)( x, y)( y')(2) + u(3)( x, y)( y')(3). We calculate the 1st nontrivial differential invariant of this action. It is a horizontal differential 2-form with values in some algebra, it is defined on the bundle of 2-jets of sections of the bundle under consideration. We prove that this form is a unique obstruction to linearizability of these equations by point transformations.