Ordinary Differential Equations, MATH 304

Homework Assignment #2

Due Friday, September 19, 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 1.3
Problems:   2, 4, 8, 13, 14*, 15*, 16, 18*

Section 1.4
Problems:   2*, 4, 5, 6*, 14, 15

Note: You may use the Existence and Uniqueness Theorem from Section 1.5 to help answer some of these questions.

Section 1.5
Problems:   2, 4, 9, 10*, 11, 18*

Section 1.6
Problems:   4, 6, 8*, 16, 18, 20*

Additional Problem: Prove that if y(t) is a solution to dy/dt = f(t), then so is y(t) + c for any real number c. This shows that solutions to ODE's of the form dy/dt = f(t) can be vertically shifted any amount. (See class notes from 9/6.)