  The role of Schwarzian derivative in the study of nonlinear ordinary
differential equations is revisited. Solutions and invariances admitted by
Painlev\'e XXV-Ermakov equation, Ermakov equation and third order linear
equation in a normal form are shown to be based on solutions of the Schwarzian
equation. Starting from the Riccati equation and the second order element of
the Riccati chian as the simplest examples of linearizable equations, by
introducing a suitable change of variables, it is shown how the Schwarzian
derivative represents a key tool in the construction of solutions. Two families
of B\"acklund transformations which link the linear and nonlinear equations
under investigation are obtained. Some examples with relevant applications are
given and discussed.
