  Sharp versions of some classical results in differential equations are given.
Main results consists of a Clunie and a Mohon'ko type theorems, both with sharp
forms of error terms. The sharpness of these results is discussed and some
applications to nonlinear differential equations are given in the conluding
remarks. Moreover, a short introduction on the connection between Nevanlinna
theory and number theory, as well as on their relation to differential
equations, is given. In addition, a brief review on the recent developments in
the field of sharp error term analysis is presented.
