The deficiencies of meromorphic solutions of certain algebraic differential equations

We use the spread relation to prove estimates that contain the Nevanlinna deficiencies of values of meromorphic solutions of certain differential equations of the form (1.1) below. We construct examples which show that all of our estimates are sharp, and in most of these constructions we use functions which are extremal for the spread relation. Several other examples are also given to illustrate our results.