  We study the structure of the solution sets in universal differential fields
of certain differential equations of order two, the Poizat equations, which are
particular cases of Li\'enard equations. We give a necessary and sufficient
condition for strong minimality for equations in this class and a complete
classification of the algebraic relations for solutions of strongly minimal
Poizat equations. We also give an analysis of the non strongly minimal cases as
well as applications concerning the Liouvillian and Pfaffian solutions of some
Li\'enard equations.
