How do I prove that the $2^{nd}$ order ODE
$$\ddot{x}(t) - \sin(x(t)) = \sin(t)$$
has no solutions $~\{x(0),\dot{x}(0)\} \in \mathbb{R}^2~$ for which $|x(t)| < \frac{\pi}{2} \quad \forall \ t\in[0,\infty]~$?
2026-03-27 20:19:41.1774642781
Proving differential equation has no bounded solutions
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