I am stuck on the following question:
Assuming $\frac{d^2y}{dx^2}-q(x)y = 0,\;\; 0 \le x \lt \infty ,\;\;y(0)=1,\;\;y'(0)=1$ wherein $q(x)$ is monotonically increasing continuous function,then which one of the following is true.
(a) $y(x) \to \infty$ as $x \to \infty$
(b) $\frac{dy}{dx}\to \infty$ as $x \to \infty$
(c) $y(x)$ has finitely many zeros in $[0,\infty)$
(d) $y(x)$ has infinitely many zeros in $[0,\infty)$
I am completely stuck on it.can anyone help me please.