Let y: ℝ → ℝ be differentiable and satisfy the ODE:
\(\left.\begin{array}{l} \frac{d y}{d x}=f(y), x \in \mathbb{R} \\ y(0)=y(1)=0 \end{array}\right\}\)
where f : ℝ → ℝ is a Lipschitz continuous function. Then
1
y(x) = 0 if and only if x ∈ {0, 1}
2
y is bounded
3
y is strictly increasing
4
dy/dx is unbounded
5
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