Consider the differential equation $y ^ { \prime }$ = g(y) where g(y) is the function whose graph is shown below:
Indicate whether the following statements are true or false.
-y = 2 is the only constant solution of $y ^ { \prime }$ = g(y) .

Question

Consider the differential equation $y ^ { \prime }$ = g(y) where g(y) is the function whose graph is shown below: 
Indicate whether the following statements are true or false.
-y = 2 is the only constant solution of $y ^ { \prime }$ = g(y) .

Quizplus · Accepted Answer

The statement that $y = 2$ is the only constant solution of $y' = g(y)$ cannot be determined as true or false without knowing the specific form of the function $g(y)$. Different functions $g(y)$ could have different constant solutions or none at all.

Consider the Differential Equation y′y ^ { \prime }y′ = G(y) Where G(y) Is the Function Whose Graph Is

Consider the Differential Equation $y ^ { \prime }$ = G(y) Where G(y) Is the Function Whose Graph Is