Hill, G. W. "On the Part of the Motion of Lunar Perigee Which is a Function of the Mean Motions of the Sun and Moon." Acta
Math.8, 1-36, 1886.Ince, E. L. Ordinary
Differential Equations. New York: Dover, p. 384, 1956.Magnus,
W. and Winkler, S. Hill's
Equation. New York: Dover, 1979.Zwillinger, D. Handbook
of Differential Equations, 3rd ed. Boston, MA: Academic Press, p. 123,
1997.
![(d^2y)/(dx^2)+[theta_0+2sum_(n=1)^inftytheta_ncos(2nx)]y=0,](/images/equations/HillsDifferentialEquation/NumberedEquation1.svg)
are fixed constants. A general solution can be given by taking the "determinant"
of an infinite matrix.
term is present, the equation have solution
are included, the equation becomes the Mathieu
differential equation, which has solution
are included, it becomes the Whittaker-Hill
differential equation.
