  A differential-algebraic geometric analogue of the Dixmier-Moeglin
equivalence is articulated, and proven to hold for $D$-groups over the
constants. The model theory of differentially closed fields of characteristic
zero, in particular the notion of analysability in the constants, plays a
central role. As an application it is shown that if $R$ is a commutative affine
Hopf algebra over a field of characteristic zero, and $A$ is an Ore extension
to which the Hopf algebra structure extends, then $A$ satisfies the classical
Dixmier-Moeglin equivalence. Along the way it is shown that all such $A$ are
Hopf Ore extensions
