Math 331.1 Problem Set 2 Fall 2005
Due: Friday, Sept. 23, start of class
1. Do page 63, Exercise 2.
2. Do page 64, Exercise 12.
3. For the initial value problem equation y=y2/3,y(0)=0:
(a) Verify that y1(t) = 0 is a solution.
(b) Verify that y2(t)= 1
27 t3is also a solution.
(c) Why doesn’t this situation contradict the Uniqueness Theorem?
(d) What does HPGSolver (from DETools) do with this problem?
4. Do page 74, Exercise 12.
5. (a) Do page 91, Exercise 4.
(b) Do page 92, Exercise 16. You should make a sketch with paper and
pencil here that is qualitatively correct and based upon the nature
of the equilibrium points. Thus, you could determine for each of
the solutions y(t) at issue what the values of limt→∞ y(t) and
limt→−∞ y(t) are—and include some words of justification . (Of
course, you may check your sketch against what your calculator
or some ODE graphing applet shows.)
6. Do page 92, Exercise 30. Note that the graph shown for f(y) is tangent
to the horizontal axis at the rightmost bend.