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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

  1. $y(x)=0$ if and only if $x\in {0,1} $
  2. $y$ is bounded.  
  3. $y$ is strictly increasing.
  4. $\frac{dy}{dx}$ is unbounded
in Differential Equation by Expert | 60 views

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