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Differential Equations

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Moderate

Lyapunov Function With Positive Definite Derivative

DIFFEQ-CMP7LM

$\dot{x}=2x^2y+y^3$,
$\dot{y}=-2xy^2+2x^5$.

Using the function $V=xy$, we can determine that $(0,0)$ is

A

stable.

B

asymptotically stable.

C

unstable.

D

$V$ is not even positive definite, and this is a poor Lyapunov function.