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

The Ermakov-Pinney Equation: its varied origins and the effects of the introduction of symmetry-breaking functions