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Differential Equations

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Identifying Critical Points

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Consider the following first order autonomous nonlinear system

$$ \left\{ \begin{array}{c} \cfrac{dx}{dt}=(1+y)\sin x,\\\ \cfrac{dy}{dt}=1-\cos x-y. \end{array}\right. $$
Consider two points $P_1(0,0)$ and $P_2(\frac{\pi}{2}, -1)$. Are they critical points of the system?

A

Only $P_1$

B

Only $P_2$

C

Neither $P_1$ nor $P_2$

D

Both $P_1$ and $P_2$