(a) What can you say about a solution of the equation y' = (1/3)y2 just by looking at the differential equation? O The function y must be strictly decreasing 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. The function y must be decreasing (or equal to 0) on any interval on which it is defined. (b) Verify that all members of the family y = 3/(x + C) are solutions of the equation in part (a). y = 3 X+C y' = (x+c)2 LHS = y=- (x + C) x + C 1) = -1/3/2 = 1 RHS (c) Can you think of a solution of the differential equation y = (1/3)y2 that is not a member of the family in part (b)? Oy = ex is a solution of y' = (1/3)y2 that is not a member of the family in part (b). Every solution of y' = (1/3)y2 is a member of the family in part (b). O y = 0 is a solution of y' = O y = x is a solution of y = O y = 3 is a solution of y' = (1/3)y2 that is not a member of the family in part (b). (1/3)y2 that is not a member of the family in part (b). (1/3)y2 that is not a member of the family in part (b). (d) Find a solution of the initial-value problem. y' = (1/3)y y(0) = 0.1