Ordinary Differential Equations, MATH 304

Homework Assignment #5

Due Friday, October 24, 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.

Note: For the problems that ask for a sketch using ``HPGSystemSolver,'' it is fine to print out a figure from that program. In other words, you do not need to copy the figure by hand onto your homework. Please be organized with how you submit your solutions.

Section 2.1
Problems:   1, 2*, 4, 6, 8*, 20*

Section 2.2
Problems:   8, 10, 11*, 14, 18*, 19, 21*, 23, 24

Section 2.3
Problems:   2*, 3, 5

Section 2.4
Problems:   3, 4*

Hint: To check that a given pair of functions is a solution to a system, determine whether they satisfy both equations simultaneously.

Section 2.5
Problems:   4*, 5

Note: When using ``EulersMethodForSystems'' (book software), the program only computes the result of one step of Euler's method. Thus, in order to determine the entire approximate solution, you will need to enter the result of each step as a new initial condition n different times.

Section 2.6
Problems:   2, 8*