MathDB

26

Part of 1991 Arnold's Trivium

Problems(1)

Problem 26

Source:

7/1/2010
Investigate the behaviour as t→+∞t\to+\infty of solutions of the systems
{x˙=yy˙=2sin⁡y−y−x\begin{cases} \dot{x}=y\\ \dot{y}=2\sin y-y-x\end{cases}
{x˙=yy˙=2x−x3−x2−ϵy\begin{cases} \dot{x}=y\\ \dot{y}=2x-x^{3}-x^{2}-\epsilon y\end{cases}
where ϵ≪1\epsilon\ll 1.
trigonometry