The geometric configuration of the solutions of $\frac { d x } { d t } = 5 x + y , \frac { d y } { d t } = 3 x + 3 y$ in the phase plane is
A) stable spiral point
B) unstable spiral point
C) stable node
D) unstable node
E) saddle point

Question

Quizplus · Accepted Answer

The system of differential equations can be written in matrix form and the eigenvalues of the matrix determine the type of equilibrium point. The eigenvalues are real and positive, indicating an unstable node.

The Geometric Configuration of the Solutions Of dxdt=5x+y,dydt=3x+3y\frac { d x } { d t } = 5 x + y , \frac { d y } { d t } = 3 x + 3 ydtdx​=5x+y,dtdy​=3x+3y

The Geometric Configuration of the Solutions Of $\frac { d x } { d t } = 5 x + y , \frac { d y } { d t } = 3 x + 3 y$