On the Automorphism Group of a polynomial differential ring in two variables

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