On Lie’s problem and differential invariants of ODEs $y''=F(x,y)$

A point classification of ordinary differential equations of the form $y''=F(x,y)$ is considered. The algebra of differential invariants of the action of the point symmetry pseudogroup on the right-hand sides of equations of the form $y''=F(x,y)$ is calculated, and Lie's problem on the point equivalence of such equations is solved.