  We consider differential rings of the form (K[x; y];D), where K is an
algebraically closed field of characteristic zero and D : K[x; y] \to K[x; y]
is a K-derivation. We study the Automorphism Group of such a ring and give
criteria for deciding whether that group is an algebraic group. In most cases,
from that study we deduce a primary classification of this type of differential
ring up to conjugation with a polynomial automorphism.
