Poizat proved that the only infinite differential algebraic subvariety of $xx^{\prime\prime}=x^\prime$ is the field of constants. His proof was a complicated computational argument. We give an easy algebraic proof of this result and completely characterize for which complex rational functions $f(x)$ the differential equation $x^{\prime\prime}/x^\prime=f(x)$ is strongly minimal. An application is given to certain Lienard equations.

We go on to examine algebraic relations between solutions of these equations and to look at some of the non strongly minimal cases. This is joint work with Jim Freitag, Remi Jaoui and Ronnie Nagloo.