  We discuss how the geometric theory of differential equations can be used for
the numerical integration and visualisation of implicit ordinary differential
equations, in particular around singularities of the equation. The Vessiot
theory automatically transforms an implicit differential equation into a vector
field distribution on a manifold and thus reduces its analysis to standard
problems in dynamical systems theory like the integration of a vector field and
the determination of invariant manifolds. For the visualisation of
low-dimensional situations we adapt the streamlines algorithm of Jobard and
Lefer to 2.5 and 3 dimensions. A concrete implementation in Matlab is discussed
and some concrete examples are presented.
