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

question 70

Multiple Choice

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