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

question 18

Multiple Choice

Which of the following systems are autonomous? Select all that apply.

• A) \(\frac { d x } { d t } = x + y , \frac { d y } { d t } = 2 t - 3 \sin t\)
• B) \[\frac { d x } { d t } = 3.5 x + 2 y , \frac { d y } { d t } = 2 x - 5 y\]
• C) \(\frac { d x } { d t } = x + y , \frac { d y } { d t } = 2 x e ^ { t } - 3 y\)
• D) \(\frac { d x } { d t } = 0 , \frac { d y } { d t } = 2 \cos x - 3 y\)
• E) \(\frac { d x } { d t } = t ^ { 2 } + 1 , \frac { d y } { d t } = 15 x - 4 y\)

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Definitions:

Temperature

A measure of the thermal energy of a substance or system, indicating how hot or cold it is.

Temperature Doubles

Refers to the scenario where the temperature of a system or substance is increased to twice its initial value.

Volume

The volume of space taken up by an object or material.

Volume Increases

A physical change where the amount of space that a substance or object occupies becomes larger.