Hill differential equation

This article is about the Hill differential equation; for the equation used in biochemistry see Hill equation (biochemistry)

In mathematics, the Hill equation or Hill differential equation is the second-order linear ordinary differential equation

where f(t) is a periodic function. It is named after George William Hill, who introduced it in 1886.

One can always assume that the period of f(t) equals π; then the Hill equation can be rewritten using the Fourier series of f(t):