I read Coddington, theory of ordinary differential equations. And there is a statement that
"A zero of a nontrivial solution of $$ (p(t)x(t)')'+g(t)x(t)=0,\quad p(t)>0,\quad p, p', g\in \mathcal{C}(a,b). $$ is isolated. Indeed, let the solution $\phi$ vanishes at $t_0.$ Then $\phi'(t_0)\neq 0$, for otherwise $\phi(t):=0.$ This proves that $t_0$ is an isolated zero."
I think that if zeros are discrete, then zeros are isolated, but I don't know how to start.
Please give me any hint.