  Transformations of differential equations to other equivalent equations play
a central role in many routines for solving intricate equations. A class of
differential equations that are particularly amenable to solution techniques
based on such transformations is the class of linearisable second-order
ordinary differential equations (ODEs). There are various characterisations of
such ODEs. We exploit a particular characterisation and the expanded Lie group
method to construct a generic solution for all linearisable second-order ODEs.
The general solution of any given equation from this class is then easily
obtainable from the generic solution through a point transformation constructed
using only two suitably chosen symmetries of the equation. We illustrate the
approach with three examples.
