Identify equilibrium values and determine which are stable and which are unstable.
-$$y ^ { \prime } = \sqrt { 7 y } , y 0$$
A) y = 0 is an unstable equilibrium value.
B) y = 7 is an unstable equilibrium value.
C) y = 0 is a stable equilibrium value.
D) There are no equilibrium values.

Question

Identify equilibrium values and determine which are stable and which are unstable.
-$$y ^ { \prime } = \sqrt { 7 y } , y > 0$$
A) y = 0 is an unstable equilibrium value.
B) y = 7 is an unstable equilibrium value.
C) y = 0 is a stable equilibrium value.
D) There are no equilibrium values.

Quizplus · Accepted Answer

For an equilibrium value, $ y' = 0 $. Since $ y' = \sqrt{7y} $, it is zero only when $ y = 0 $. However, $ y > 0 $ is given, so there are no equilibrium values in the domain.

Identify Equilibrium Values and Determine Which Are Stable and Which y′=7y,y>0y ^ { \prime } = \sqrt { 7 y } , y > 0y′=7y​,y>0

Identify Equilibrium Values and Determine Which Are Stable and Which $y ^ { \prime } = \sqrt { 7 y } , y > 0$