  We consider the generalized Painlev\'e--Ince equation, \begin{equation*}
\ddot{x}+\alpha x\dot{x}+\beta x^{3}=0 \end{equation*} and we perform a
detailed study in terms of symmetry analysis and of the singularity analysis.
When the free parameters are related as $\beta =\alpha ^{2}/9~$the given
differential equation is maximally symmetric and well-known that it pass the
Painlev\'{e} test. For arbitrary parameters we find that there exists only two
Lie point symmetries which can be used to reduce the differential equation into
an algebraic equation. However, the generalized Painlev\'{e}--Ince equation
fails at the Painlev\'{e} test, except if we apply the singularity analysis for
the new second-order differential equation which follows from the change of
variable $x=1/y.$ We conclude that the Painlev\'{e}--Ince equation is
integrable is terms of Lie symmetries and of the Painlev\'{e} test.

Exactly Solvable and Integrable Systems;Classical Analysis and ODEs