Galois differential group

The group of all automorphisms of a differential field $P$ that commute with derivations (cf. Derivation in a ring) and that leave all elements of some fixed differential subfield of $P$ invariant.

Comments

Just as Galois theory has things to say about (solving) algebraic equations, so differential Galois theory (or the Galois theory of differential fields) is relevant to (solving) algebraic differential equations. For an account of differential Galois theory see Extension of a differential field and the references given there.