a) What can you say about a solution of the equation y' = −(1/2)y2 just by looking at the differential equation? The function y must be strictly decreasing on any interval on which it is defined. The function y must be decreasing (or equal to 0) on any interval on which it is defined. The function y must be increasing (or equal to 0) on any interval on which it is defined. The function y must be strictly increasing on any interval on which it is defined. The function y must be equal to 0 on any interval on which it is defined. (b) Verify that all members of the family y = 2/(x + C) are solutions of the equation in part (a). y = 2 x + C ⇒ y' = − (x + C)2 . LHS = y' = − (x + C)2 = − 1 2 x + C 2 = − 1 2 y2 = RHS (c) Can you think of a solution of the differential equation y' = −(1/2)y2 that is not a member of the family in part (b)? y = 2 is a solution of y' = −(1/2)y2 that is not a member of the family in part (b). y = e2x is a solution of y' = −(1/2)y2 that is not a member of the family in part (b). y = 0 is a solution of y' = −(1/2)y2 that is not a member of the family in part (b). y = x is a solution of y' = −(1/2)y2 that is not a member of the family in part (b). Every solution of y' = −(1/2)y2 is a member of the family in part (b). (d) Find a solution of the initial-value problem. y' = −(1/2)y2 y(0) = 0.5 y =