XSXC


Assignment 1:  Due Jan 29

1.  page 24 #1-6

2.  page 15 #1

3.  page 16 #6 (needs #4 and #5 

4.  Use dfield (or any program which draws direction fields) to draw
    graph a direction field  for

                 y' = (10 - y)(y)(2-y)

Identify the equilibrium (fixed points) for the equation and decide whether
nearly solutions are approaching or leaving the equilibrium points. Graph
the three solutions which pass through the point (0,1), (0,4) and (0,11).

5. page 10 #30.

Note that you may have to change the endpoints of the interval on which
t and y are graphed to give a proper answer to #4, #5.

Extra credit (hand in separately to Professor Uhlenbeck).

Find the general soution to the equation y' = y(1 - y^2) and describe
the behavior of the solutions for large t. (The computer might help
you check your work).