Differential invariants and equivalence of ODEs $y^{\prime \prime }=a^3(x,y)y^{\prime 3}+a^2(x,y)y^{\prime 2}+a^1(x,y)y^{\prime }+a^0(x,y)$

Abstract

This paper is devoted to ordinary differential equations of the form $$y^{\prime \prime }=a^3(x,y)y^{\prime 3}+a^2(x,y)y^{\prime 2}+a^1(x,y)y^{\prime }+a^0(x,y)$$ The algebra of all differential invariants of point transformations is constructed for these equations in general position and the equivalence problem is solved for them.