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

question 27

Multiple Choice

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) \(\frac { d x } { d t } = t + 1 , \frac { d y } { d t } = 15 x - 4 y\)

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Definitions:

Achilles Reflex

A reflex action of the foot, elicited by a sudden stretch of the Achilles tendon, indicating normal function of the lower segment of the spinal cord.

Plantar Reflex

A reflex elicited by stroking the sole of the foot, used to assess the integrity of the spinal cord and higher brain centers; a normal response curls the toes, while the Babinski sign indicates neurological concerns.

Biceps Reflex

A reflex test that evaluates the function of the spinal cord by striking the biceps tendon and observing arm movement.

Sigmoidoscopy

A medical procedure involving the examination of the lower part of the large intestine using a flexible tube with a light and camera.