Let $y: \mathbb{R}\rightarrow \mathbb{R}$ be differentiable with $y(0)=y(1)=0$ and satisfy the ODE: $$\frac{dy}{dx}=f(y),\quad x \in \mathbb{R} $$ Suppose $f:\mathbb{R}\rightarrow \mathbb{R}$ is a Lipschitz condition function. Then

- $y(x)=0$ if and only if $x\in {0,1} $
- $y$ is bounded.
- $y$ is strictly increasing.
- $\frac{dy}{dx}$ is unbounded