In mathematics, in the field of ordinary differential equations, a nontrivial solution to an ordinary differential equation

${\displaystyle F(x,y,y',\ \dots ,\ y^{(n-1)})=y^{(n)}\quad x\in [0,+\infty )}$

is called oscillating if it has an infinite number of roots; otherwise it is called non-oscillating. The differential equation is called oscillating if it has an oscillating solution. The number of roots carries also information on the spectrum of associated boundary value problems.