  We provide a characterisation of differentially large fields in arbitrary
characteristic and a single derivation in the spirit of Blum axioms for
differentially closed fields. In the case of characteristic zero, we use these
axioms to characterise differential largeness in terms of being existentially
closed in the differential algebraic Laurent series ring, and we prove that any
large field of infinite transcendence degree can be expanded to a
differentially large field even under certain prescribed constant fields. As an
application, we show that the theory of proper dense pairs of models of a
complete and modelcomplete theory of large fields, is a complete theory. As a
further consequence of the expansion result we show that there is no real
closed and differential field that has a prime model extension in closed
ordered differential fields, unless it is itself a closed ordered differential
field.
