  We introduce a general notion of solution for a Noetherian differential
$k$-algebra and study its relationship with simplicity, where k is an
algebraically closed field; then we analyze conditions under which such
solutions may exist and be unique, with special emphasis in the cases of
k-algebras of finite type and formal series rings over k. Using that notion we
generalize a criterion for simplicity due to Brumatti-Lequain-Levcovitz and
give a geometric characterization of that; as an application we give a new
proof of a classification theorem for local simplicity due to Hart and obtain a
general result for simplicity of formal series rings over k
