Galois differential group
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.
Galois differential group. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Galois_differential_group&oldid=15153