  In [DL] systems of differential polynomials are investigated with respect to
properties of Artin approximation type. The key tool in [DL] is an extended
version of a formula by Hurwitz [Hu] expressing high order derivatives of an
expansion by lower ones. The formula is further refined in [VFZ] to deliver
sufficient conditions concerning the existence of power series solutions of
scalar algebraic differential equations of order n. In the paper at hand, the
main results from [VFZ] are first reproduced and further extended to systems of
nonlinear differential algebraic equations. In addition, a simple extension of
Tougeron's implicit function theorem is given in a specific constellation. The
results follow from [S1], [S2] where Artin approximation is treated within a
Banach space setting, thereby constructing an expansion formula that expresses
accurately the required dependency of low and high order derivatives within the
system of undetermined coefficients.
