Could anyone comment on the following exercise from ODE?
For any $\epsilon > 0$, find $\delta > 0$ such that $\ddot{X}+X-2X^{3}=0$ and $\sqrt{X^{2}(0)+\dot{X}^{2}(0)}< \delta \Rightarrow \sqrt{X^{2}(t)+\dot{X}^{2}(t)}< \epsilon$, for all $t \geq 0$.
Thank you!