I will discuss the following theorem: if $T$ is a model-complete theory of fields which are large (in the sense of Pop) and and bounded (in the sense of small Galois group), and $T_D$ is the model companion of the theory $T$ + "$D$ is a derivation", THEN any model $K$ of $T_D$ is Picard-Vessiot closed, in the sense that any linear differential equation over $K$ has a fundamental system of solutions in $K$ (and likewise for a more general class of differential equations).