A differential equation is disintegrated (or geometrically trivial) if any algebraic relation between an arbitrary number of its solutions can be decomposed into algebraic relations between couples of solutions.

In my talk, I will discuss certain geometric notions, coming from the theory of foliations on smooth algebraic varieties, which provide effective techniques to study this property for autonomous algebraic differential equations.

I will also describe applications of these techniques to the study of planar algebraic vector fields and of certain families of three-dimensional algebraic differential equations.