Note: I have listed good problems for practice as "Do these problems". You only need to hand in the problems labeled "To turn in".

 
Exercises from Section 2.1 page 39-41: 
Do these problems: 6,13,15,17,21,31,34,35.
To turn in: 6, 15, 21, 31, 34, 35
Comments: #6: use a computer to draw the direction field for part a).
         #21: use a computer to draw the direction field for you.  
          Use screen capture to create your printout for both of 
          these problems.  Answer the questions in part a) with words.  
         #34,35: These are "backward problems".  We try to find the ODE 
         that gives the desired solutions instead of finding the solution
         to the ODE.  One approach is to look through previous problems
         to find similar solution behavior and the tweak the problem to get
         these exact behaviors.  Another is to try to think about what
         y' should be when y is the desired long term solution.  Then make
         sure y' is the right size on either side of that long term behavior
         so that all solutions tend toward that long term solution.

 
Exercises from Section 2.2 page 47-50:
Do these problems: 8,10,12,21,23,26,30.
To turn in: 8, 10ac, 21, 23, 30a-e
Comments: #21: In the hint, "integral curve" just means "trajectory" so
         the hint says to look for values where y' is infinite(doesn't exist).
         #30:  Parts b) and c) are closely linked here so if you have trouble
         with what b) is asking look at c).  Also for c) show that the second
         equation is obtained from the first equation.

Exercises from Section 2.3 page 59-68:
Do these problems: 9, 10, 14
To turn in: 14a

Exercises from Section 2.4 page 75-77:
Do these problems: 2,8,13,22,24,25,26,28,32.
To turn in: 13, 22, 24, 28
Comments: #28: This problem clearly depends on #27, so read through that.
               The solution method is essentially a u-substitution but for
               an ODE instead of an integral.  We are changing variables
               from y to v (don't forget to find y' in terms of v' also).
               The resulting ODE for v should be linear (as 27b suggests).

Extra Problem

This extra problem should be turned in with the others.
The equation dy/dt = 1/(1+y), with initial condition y(0)=-1 has two solutions.
a) Find both solutions analytically.  

Now solve the system using a computer (e.g. the 
    ODE solver 
    by some good folks at University of Applied Sciences, Dresden Germany.)
The computer will compute dy/dt to be Inf (infinity) so you will have to 
start close to -1 but not at it to even get a numerical solution.
(Answer with a paragraph using complete sentences.  You don't need to 
hand in the pictures.)

b) Which solution does the computer find?  
c) How can you trick the computer into finding both solutions?