Which of the following systems are autonomous? Select all that apply.
A) $\frac { d x } { d t } = x + y ^ { 2 } , \frac { d y } { d t } = 2 x - 3 y$
B) $\frac { d x } { d t } = x + t , \frac { d y } { d t } = 2 x - 3 y$
C) $\frac { d x } { d t } = x + y , \frac { d y } { d t } = 2 x - 3 y$
D) $\frac { d x } { d t } = 0 , \frac { d y } { d t } = 2 \sin x - 3 y$
E) $\frac { d x } { d t } = t + 1 , \frac { d y } { d t } = 15 x - 4 y$

Question

Quizplus · Accepted Answer

An autonomous system is one where the derivatives of the variables are functions of the variables themselves and do not explicitly depend on the independent variable (often time, t). Choices A, C, and D fit this description as their derivatives depend only on x and y, not explicitly on t.

Which of the Following Systems Are Autonomous? Select All That dxdt=x+y2,dydt=2x−3y\frac { d x } { d t } = x + y ^ { 2 } , \frac { d y } { d t } = 2 x - 3 ydtdx​=x+y2,dtdy​=2x−3y

Which of the Following Systems Are Autonomous? Select All That $\frac { d x } { d t } = x + y ^ { 2 } , \frac { d y } { d t } = 2 x - 3 y$