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In the present paper we consider the problem of local equivalence of secondorder ODEs which are cubic in second derivative under the action of thepseudogroup of contact transformations. We show how it may be reduced to theequivalence problem of 2-webs in $\mathbb{R}^3$ under the action offinite-dimensional group, admitted by the associated second order equation.

The action of contact transformations pseudogroup on the second order ODEs which are cubic in second derivative