This assignment is not as long as the last one, but it still will take substantial time. Start early to relieve time pressure and to be able to take advantage of help in office hours and in class.
Read chapter 2.2, 2.3, 2.4.
Section 1.1: Exercises 19, 24.
(Do these again, drawing the direction field and several representatative solution curves with a computer program. Carefully describe the observed behavior of the solutions in various regions, in particular their behavior as t becomes large positive and large negative.)
Section 2.2: Exercises: 3, 9, 21, 26, 28, 30.
Problems 28 and 30 are the most difficult, and deserve the most attention and time.
28c concerns the following situation: You have a certain differential equation with the property that for each y0 the solution to the initial value problem with initial value y(0) = y0 exists for all t in the interval (-1, infinity). For each y0 is is possible to evaluate the solution at t = 2. This give a new function g(y0) whose value at y0 is the value of the solution at t=2 to the IVP with initial value y0. That is g(y0) is the y coordinate at t = 2 of the solution curve thru (0, y0). The function g(y0) can be computed explicitly, and you can show that it is an increasing function of y0. You are asked to find out for which values of y0 is g(y0) in the interval 3.99 < g(y0) < 4.01.
Section 2.3 Exercises: 19, 32.
Do these exercises using Mathematica.