Ordinary Differential Equations, MATH 304

Homework Assignment #4

Due Friday, October 3, START of Class

Homework should be turned in at the BEGINNING OF CLASS. All problem numbers refer to Differential Equations, 4th ed., by Blanchard, Devaney, and Hall. Unless otherwise indicated, all parts of a problem (a), (b), etc. should be completed. You should do all of the problems; however, you only need to write up solutions for the starred (*) problems. You should also write up the solution to the additional problem based on the supplementary reading. Be sure to write up solutions neatly, making sure to show your work.

You are encouraged to work on these problems with other classmates, and it is ok to use internet sources for help if it's absolutely necessary; however, the solutions you turn in should be YOUR OWN WORK and written in YOUR OWN WORDS. Complete solutions to all problems will be posted the same day the homework assignment is due.

Important: Please list the names of any students you worked with on the assignment.

Section 1.8
Problems:   3, 6*, 12*, 17, 22*, 31

Section 1.9
Problems:   3, 4*, 8*, 11, 12*, 21

Additional Problem: Consider the periodic linear differential equation dy/dt = -2y - 2sin(2t) - cos(2t).
(a) What is the period of the differential equation?
(b) Find the general solution.
(c) Find an explicit formula for the Poincare map P(y0).
(d) Find the fixed point of P. What is the corresponding periodic solution of the ODE?