#### Vol. 15, No. 10, 2021

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Generic planar algebraic vector fields are strongly minimal and disintegrated

### Rémi Jaoui

Vol. 15 (2021), No. 10, 2449–2483
DOI: 10.2140/ant.2021.15.2449
##### Abstract

We study model-theoretic properties of algebraic differential equations of order two defined over constant differential fields. In particular, we show that the set of solutions of a “general” differential equation of order two and of degree $d\ge 3$ in a differentially closed field is strongly minimal and disintegrated (in other words, is strongly minimal with trivial forking geometry).

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.

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