Hill's differential equation

This article deals with a common differential equation named after George William Hill. For a differential equation named after him from celestial mechanics, see Hill's differential equation (three-body problem) .

The Hill's equation is a linear ordinary differential equation of second order of the mold

${\displaystyle \ y''(x)+q(x)y(x)=0}$

where is a periodic function . It is named after George William Hill . It is particularly relevant for problems related to vibration theory. ${\displaystyle q(x)}$

See also

• Mathieu differential equation
• Parametric oscillator
• Sturm Liouville Problem

credentials

• W. Magnus, S. Winkler: Hill's equation . Interscience Publishers John Wiley & Sons, New York-London-Sydney 1966.
• Gerald Teschl : Ordinary Differential Equations and Dynamical Systems . American Mathematical Society , Providence 2012, ISBN 978-0-8218-8328-0 .