Name_____________________________       UTEID____________________

Math 427K           Uhlenbeck    Due April 21, 2005   Homework 9

Please answer the questions on the problem sheet and attach your work on
the back. Attach your computer work (pplane) for problems 1-3 as well. 
Use a grid size and location suitable to the question This counts).

1.  Find  and classify the critical points for the system
    x' =  x(2.4 - 1.4 x - y);  y' = y(1.8 - y - .8 x)








2.  Find  and classify the critical points for the system
    x' =  y(2.4 - 1.4 x - y);  y' = x(1.8 - y - .8 x)







3. Find and classify the critical points of the system
x' = .5 x  + y  - x(x^2 +  y^2), y' =  -3x  +.6 y  - y(x^2 + y^2).
Describe the limiting behavior of the solution curves as t goes to + infinity.
(You will have to do this using pplane).








4. Find the iterative  equation for the power series solution to
    y"(x) + xy'(x)  +  y = 0.  Assume that y(0) = 0 and y'(0) =1.
Give the first three  nonzero terms in the power series expansion.








5. Look for a cubic polynomial which solves  (1 - x^2)y" - 2xy' + 12 y = 0.