The critical point $( 0,0 )$ of the system $\frac { d x } { d t } = - 3 x + 2 y , \frac { d y } { d t } = 4 x - y$ is Select all that apply.
A) asymptotically stable
B) stable but not asymptotically stable
C) unstable
D) an attractor
E) a repeller

Question

Quizplus · Accepted Answer

The eigenvalues of the system's matrix are $\lambda_1 = 1$ and $\lambda_2 = -5$, indicating a saddle point, which is unstable.

The Critical Point (0,0)( 0,0 )(0,0) Of the System dxdt=−3x+2y,dydt=4x−y\frac { d x } { d t } = - 3 x + 2 y , \frac { d y } { d t } = 4 x - ydtdx​=−3x+2y,dtdy​=4x−y

The Critical Point $( 0,0 )$ Of the System $\frac { d x } { d t } = - 3 x + 2 y , \frac { d y } { d t } = 4 x - y$