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.
-Let $y ^ { \prime }$ = 2 - y. Which of the following properties hold for the solution y = f(t) determined by the initial condition y(0) = 1? (I) It is always concave down.
(II) It is a constant solution.
(III) It is always decreasing.
A) I only
B) III only
C) I and III
D) II only
E) none of these

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.
-Let $y ^ { \prime }$ = 2 - y. Which of the following properties hold for the solution y = f(t) determined by the initial condition y(0) = 1? (I) It is always concave down.
(II) It is a constant solution.
(III) It is always decreasing.
A) I only 
B) III only 
C) I and III 
D) II only 
E) none of these

Quizplus · Accepted Answer

The solution to the differential equation $y' = 2 - y$ is $y = 2 - Ce^{-t}$. This function is concave down because its second derivative is negative. It is not constant and not always decreasing.

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