NAME______________________________________  UTEID__________

427K   Uhlenbeck   Homework   2  Due 2/3/05

Go to the computer lab in RLM 8.136 and obtain a mathematics computer
account, or use your own version of matlab.  Get directions on how to
login and use your account from the lab proctors.

Answer the five following questions by producing a direction field for
the given ordinary differential equation and graphing the relevant
solutions.  Print your plots and staple all five of them to this
sheet. Answer the questions on this sheet.

Directions: a) Login.  b) Type "matlab" and wait.  c)Type "dfield" and wait. 
d) Replace the differential equation  x' = x^2 - t  by the
differential equation  for which you wish to plot the  direction field
and solutions.     e)  Adjust the t range and the x range  by trial and
error (You will not have to do this on the first problem).  f) Click on
Continue.  g) Click with the right button on the initial points for
the solutions you wish to graph.  h) Print the plot you wish to hand in
by clicking on print.  i) Click on quit.  START AGAIN AT c).

1.  Plot a number of  solutions to  y' =  -0.4*y + 0.5. Describe the
behavior of the solutions as to goes to infinity.





2.  Plot  two solutions to  y' =  .2*y*(3 - y).  Plot the solution
with y(0) = 1. What is the limit as t goes to infinity?  At what time
(approximately) is the solution y(t) = 2? 





3.  Plot the solutions to  y' = -.2*y  +  sin(t).  Include the solution
with y(0) = 2 and the solution with y(0) = - 2.  Describe the limit as
t goes to infinity of the solutions (Use a scale for your graph that makes
the behavior as t goes to infinity clear.)






4.Do problem 1 on page 59, but find the time needed for the dye in the
tank to reach 10% of its original value (not 1% which is hard to find 
on a graph). Graph your solution and mark the solution time on the 
graph.




5.Do problem 11 on page 61 using dfield. (There is no need to get an exact
solution to either part).