Chapter 11.8, Problem 12E

In equation $\left(10\right)$, assume $Q\left(x\right)\ge m^2$ on $\left[a,b\right]$. Prove that the distance between two consecutive zeros of a solution $\varphi$ to $\left(10\right)$ is less than or equal to $\text{π}/m$. [Hint: If $x_1$ is a zero of $\varphi$, compare $\varphi$ with the function $\psi \left(x\right)=\sin \left[m\left(x-x_1\right)\right]$, which is a solution to $y^{″}+m^{2}y=0$.]

$y^2+Q\left(x\right)y=0$, $a<x<b$, (10)