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(i) Consider
$\frac{d u}{d t}=\cos (u)$
where $u(t=0)=u_{0}>0$. Find the fixed points of the differential equation.
(ii) Calculate the Gateaux derivative of
$\frac{d u}{d t}-\cos (u)$
and thus find the variational equation. Study the stability of the fixed points.
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