  We study the internal structure of enveloping algebras of preLie algebras. We
show in particular that the canonical projections arising from the
Poincar\'e-Birkhoff-Witt theorem can be computed explicitely. They happen to be
closely related to the Magnus formula for matrix differential equations.
Indeed, we show that the Magnus formula provides a way to compute the canonical
projection on the preLie algebra. Conversely, our results provide new insights
on classical problems in the theory of differential equations and on recent
advances in their combinatorial understanding.
