Let k be a field of characteristic zero, f(X,Y),g(X,Y)is an element ofk[X,Y], g(X,Y)is not an element of(X,Y) and d := g(X,Y) partial derivative/partial derivativeX + f(X,Y) partial derivative/partial derivativeY. A connection is established between the d-simplicity of the local ring k[X,Y]((X,Y)) and the transcendency of the solution in tk[[t]] of the algebraic differential equation g(t,y(t))(.)(partial derivative/partial derivativet)y(t) = f (t,y(t)). This connection is used to obtain some interesting results in the theory of the formal power series and to construct new examples of differentially simple rings.683615630