Chapter 11.8, Problem 2E

To determine

If the given function contradicts the theorem:

“Let $\varphi$ be a solution to $(1)$ on $\left(a,b\right)$. If $\varphi$ has an infinite number of zeroes in any closed, bounded interval $\left[a^{\prime },b^{\prime }\right]\subset \left(a,b\right)$, then $\varphi \left(x\right)\equiv 0$ in $\left(a,b\right)$.

$\frac{d}{dx}\left(p\left(x\right)\frac{dy}{dx}\right)+Q\left(x\right)y=p\left(x\right)y^{″}+p^{\prime }\left(x\right)y^{\prime }+Q\left(x\right)y$ $=0$, $a<x<b$. $(1)$”