24. By suitably renaming the constants and dependent variables in the equations and P' aP(1-aP) I' = rI(S - I) discussed in Section 1.1 in connection with Verhulst's population model and the spread of an epidemic, we can write both in the form y' = ay - by², where a and b are positive constants. Thus, (A) is of the form (C) with y = P, a = a, and b = aa, and (B) is of the form (C) with y = I, a = rS, and b = r. In Chapter 2 we'll encounter equations of the form (C) in other applications.. Choose positive numbers a and b. Construct a direction field and plot some integral curves for (C) in a rectangular region of the form {0 0. Repeat this experiment with various choices of a and b until you can state this property precisely in terms of a and b. Choose positive numbers a and b. Construct a direction field and plot some integral curves for (C) in a rectangular region of the form {0 st≤T, e≤ y ≤0} of the ty-plane. Vary a, b, T and c until you discover a common property of all solutions of (C) with y(0) < 0. (A) (B) (C)