Exercises

Note that, unless otherwise specified, all exercises are from Boyce and DiPrima, Elementary Differential Equations and Boundary Value Problems, sixth edition.Exercise 9a - Due Friday, May 28

- Section 10.1 # 9
- Section 10.2 # 13, 14, 18, 28

Exercises 8b - Due Monday, May 24

- Section 9.3 # 5, 6
- Section 9.4 # 8, 9
- Find the fixed points of the following system, classify them, sketch
the neighbouring trajectories, and fill in the rest of the phase portrait.
- dx/dt = x-y, dy/dt = x^2 -4

Exercise 8a - Due Friday, May 21

- Section 9.1 # 2ab, 5ab, 8ab
- Section 9.2 # 5ac, 6ac, 9ac, 19

Exercise 7b - Due Monday, May 17

- Section 7.5 # 7, 16
- Section 7.6 # 2, 6, 13
- Section 7.7 # [optional 7]

Exercise 7a - Due Friday, May 14

- Section 7.1 # 21
- Section 7.3 # 15, 16, 18
- Section 7.5 # 1, 4, 5

Exercise 6b - Due Monday, May 10

- Section 6.6 # 1, 6, 10, 12, 16, 18
- Section 7.1 # 1, 3, 4, 10

Exercise 6a - Due Friday, May 7

- Section 6.3 # 9, 10, 13, 16
- Section 6.4 # 5, 9, 12
- Section 6.5 # 3, 6, 12

Exercise 5b - Due Monday, May 3

- Section 6.1, Exercises 6, 7, 26, 27.
- Section 6.2, Exercise 16, 17, [optional 28], 30.

Exercise R1 - Review (will not be graded)

- Section 2.5 Exercise 26
- Section 2.10 Exercise 2,8,10,15,43
- Section 3.5 Exercise 7,27
- Section 3.6 Exercise 6,7,17
- Section 5.2 Exercise 2

Exercise 4b - Due Monday, April 26

- Section 3.7, Exercises 31, 32.
- Section 5.2, Exercise 12.
- Section 5.3, Exercises 6, 11, 18.

- Section 3.6, Exercise 31, 32.
- y
_{1}= x^{-1/2}cos(x) is one solution of the Bessel equation

x^{2}y'' + x y' + (x^{2}- 1/4) y = 0

Use reduction of order to find the general solution. - Find the general solution of

x^{2}y'' + 2x(1-3x) y' + (9x^{2}- 6x -2) y =0

using reduction of order, given that y_{1}= x e^{3x}is a solution. - Read Section 5.1 of Elementary D.E.s and B.V.Ps.
- Section 5.2, Exercises 1, 7.

- Section 3.4, Exercise 40.
- Section 3.5, Exercises 6, 13, 41.
- Section 3.6, Exercises 8, 9, 10, 15.

- Section 3.1, Exercises 3, 9, 23.
- Section 3.1, Exercises 31, 36, 40.
- Section 3.4, Exercises 3, 6, 10, 14, 22.

- Section 2.8, Exercises 18, 21.
- Section 2.8, Exercises 26, 27.
- Section 2.9, Exercises 4, 5, 15.
- Section 2.9, Exercise 38.

- Section 2.1, Exercises 13,14,28
- Section 2.1, Exercises 29,31
- Section 2.8, Exercises 3,4,8
- (Hard) Show that the differential equation

is not exact, and that the differential equation

is exact. Explain why this is possible.

- Section 2.4, Exercise 17. Section 2.5, Exercise 17.
- Section 2.6, Exercises 1, 3, 10, 21.

For the next two problems, refer to the graphs on the printed handout. - Describe the long term behavior of the solutions of y' = f(y), where f(y) is the function illustrated.
- Find an equation whose solutions have the behavior illustrated.

- Read Chapter 1 of Elementary D.E.s and B.V.Ps.
- Section 2.3, Exercises 1, 3, 5, 9, 17.
- Section 2.5, Exercises 6, 21, 27.