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

Richard Michael Morris, Peter Gavin Lawrence Leach

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…