For $(K, \partial)$ a model of $DCF_0$, $(F, \partial)$ a differential subfield with $C(F)$ algebraically closed, and $dlog_G(x)=A$ a log-differential equation over $F$, one can find a corresponding strongly normal extension of $(F, \partial)$ inside of $(K, \partial)$. We discuss a certain elementary class of differential fields (which are not necessarily differentially closed) in which one can similarly find embedded strongly normal extensions of certain differential subfields.

This is joint work with Anand Pillay.