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Differential Equations

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Moderate

Classifying Critical Points

DIFFEQ-C1NXJ6

Consider the system:

$\cfrac{dx}{dt}=-(x-y)(2-x-y)$
$\cfrac{dy}{dt}=2x(1+y)$

Which one of the following statements is incorrect?

A

$(0,0)$ is a saddle point and thus unstable.

B

$(-1,-1)$ is an asymptotically node.

C

$(0,2)$ is an asymptotically stable spiral point.

D

$(3,-1)$ is an asymptotically node.