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Found problems: 1

2017 Korea USCM, 8
Tags: differential equation , ordinary differential equation , trigonometry
$u(t)$ is solution of the following initial value problem. $$\begin{cases} u''(t) + u'(t) = \sin u(t) &\;\;(t>0),\\ u(0)=1,\;\; u'(0)=0 & \end{cases}$$ (1) Show that $u(t)$ and $u'(t)$ are bounded on $t>0$. (2) Find $\lim\limits_{t\to\infty} u(t)$ with proof.