  Solutions of an implicit ODE form a web. Already for cubic ODEs the 3-web of
solutions has a nontrivial local invariant, namely the curvature form. Thus any
local classification of implicit ODEs necessarily has functional moduli if no
restriction on the class of ODEs is imposed. Here the most symmetric case of
hexagonal 3-web of solutions is discussed, i.e. the curvature is supposed to
vanish identically. A finite list of normal forms is established under some
natural regularity assumptions. Geometrical meaning of these assumptions is
that the surface, defined by ODE in the space of 1-jets, is smooth as well as
the criminant, which is the critical set of this surface projection to the
plane.
