  The Ermakov-Pinney Equation, $$\ddot{x}+\omega^2 x=\frac{h^2}{x^3},$$ has a
varied provenance which we briefly delineate. We introduce time-dependent
functions in place of the $\omega^2$ and $h^2$. The former has no effect upon
the algebra of the Lie point symmetries of the equation. The latter destroys
the $sl(2,\Re)$ symmetry and a single symmetry persists only when there is a
specific relationship between the two time-dependent functions introduced. We
calculate the form of the corresponding autonomous equation for these cases.
