  For the implicit systems of first order ordinary differential equations on
the plane there is presented the complete local classification of generic
singularities of family of its phase curves up to smooth orbital equivalence.
Besides the well known singularities of generic vector fields on the plane and
the singularities described by a generic first order implicit differential
equations, there exists only one generic singularity described by the implicit
first order equation supplied by Whitney umbrella surface generically embedded
to the space of directions on the plane.
