  In this article, we study model-theoretic properties of algebraic
differential equations of order $2$, defined over constant differential fields.
In particular, we show that the set of solutions of a general differential
equation of order $2$ and of degree $d \geq 3$ in a differentially closed field
is strongly minimal and disintegrated.
  We also give two other formulations of this result in terms of algebraic
(non)-integrability and algebraic independence of the analytic solutions of a
general planar algebraic vector field.
