I came across the following problem that says:
Let $y:[0,1] \rightarrow \mathbb R$ be a twice continuously differentiable function such that $y''(x)-y(x)<0 $ for all $x \in (0,1)$ and $y(0)=y(1)=0.$ Then which of the following statement(s) is/are true?
(a) $y$ has at least two zeros in $(0,1)$.
(b) $y$ has at least one zero in $(0,1)$.
(c) $y(x)>0$ for all $x \in (0,1)$.
(d) $y(x)<0$ for all $x \in (0,1)$.
Can someone point me in the right direction? Thanks in advance for your time.