The homework assignments to be turned in and graded are listed below.
Homework Assignments
- Due Tuesday, January 22.
1.1 # 4, 8 (see description of the learning process on p. 15-16), 15, 16, 19, 20
1.2 # 2, 10, 12, 15, 18, 26, 30
1.3 # 2, 3, 9 (see notes below), 16, 18
Solve the differential equation dy/dx=(x^2+xy+y^2)/(x^2)
Notes about section 1.3: For # 2, 3, and 9, use Maple to draw the slope fields and 3 solution curves with different initial conditions. Don't worry about the instructions in the text. To turn in the problems, you can either sketch your slope fields and solutions on a sheet of paper, or print out your Maple file.
Homework 1 Solutions as a .pdf file
The following problems were graded for completion only. You should use the posted solutions to make sure that your solutions for these problems are correct.
1.1 # 8, 16, 20
1.2 #2, 18, 30
1.3 # 2, 3, 9, 18
- Due Tuesday, January 29.
Numerical Simulations Problem
1.5 # 4, 8, 13, 14
1.6 # 2, 8, 12, 14, 20, 37, 39, 41 (you don't need to use "PhaseLines" for this problem; just do it by hand)
Homework 2 Solutions as a .pdf file
Maple file for the Numeric Simulations Problem. This Maple worksheet is posted on the P: drive at P:/Class/Math/Paquin/DiffEq/NumericHW2.mw.
- Due Tuesday, February 5.
1.7 # 2, 4, 8, 10, 13, 14, 17. Note: For #2, 4, 8, please draw the bifurcation diagrams in addition to the phase lines.
1.8 # 2, 4, 6, 8, 19, 20, 21, 33(b). Note: For a hint on #4, see the example on p. 119 of your textbook. For a hint on #6, see the example on the bottom of p. 121.
1.9 # 2, 6, 10, 14, 16, 20
Homework 3 Solutions as a .pdf file
- Due Tuesday, February 12.
Part 1:
2.1: 1, 2, 7(a), 9-14, 17
2.2: 10, 11, 13, 16, 17. Note: For 13, 16, and 17, do the following: (a) find the equilibrium points, (b) use Maple to draw the direction field and phase portrait, and (c) use Maple to draw the x vs. t and y vs. t graphs for each system
Part 2:
2.1: 19(a),(b); 20(a)
2.2: 7(c),(d),(e); 8(c),(d),(e); 19(b),(c). Note: For these problems, use Maple instead of the HPGSystemSolver.
Homework 4 Solutions as a .pdf file
- Due Tuesday, February 19.
Part 1:
Problems 2, 6, 8, 10, 12, 14, 24 from the problem set distributed in class (Boyce and DiPrima Section 3.1). Here is the problem set as a pdf file. The answers to the problems are posted as a pdf file, so that you can check your work as you go. The answers are those listed under the "Section 3.1" heading. You can also do additional practice problems, and check your answers to those. Of course, to receive full credit for the homework problems, you need to show all of your work, not just the final answers. Note: you can ignore the posted answer for problem 24.
Part 2:
Problems 3, 4, 5, 6, 8, 12, 16, 23, 24, 25, 27 from the problem set distributed in class (Boyce and DiPrima Section 3.2). Here is the problem set as a pdf file. The answers to the problems are posted as a pdf file, so that you can check your work as you go. The answers are those listed under the "Section 3.2" heading. You can also do additional practice problems, and check your answers to those. Of course, to receive full credit for the homework problems, you need to show all of your work, not just the final answers.
- Due Tuesday, March 18.
Note: this homework will not be graded or collected (to give you time to complete the take-home midterm exam). I strongly encourage you to complete these homework problems as practice for the quiz on Thursday, March 20. The quiz on Thursday, March 20 will cover second-order linear homogeneous differential equations with constant coefficients and the reduction of order technique.
Part 1:
Problems 8, 10, 12, 18, 22, 24 from the problem set distributed in class (Boyce and DiPrima Section 3.4). Here is the problem set as a pdf file. The answers to the problems are posted as a pdf file, so that you can check your work as you go. The answers are those listed under the "Section 3.4" heading. You can also do additional practice problems, and check your answers to those.
Part 2:
Problems 1-13 odd, 16, 17 from the problem set distributed in class (Boyce and DiPrima Section 3.5). Here is the problem set as a pdf file. The answers to the problems are posted as a pdf file, so that you can check your work as you go. The answers are those listed under the "Section 3.5" heading. You can also do additional practice problems, and check your answers to those.
Part 3:
Reduction of order practice problems. These are some practice problems for the reduction or order technique. The answers are posted as well (second page of the same file), so that you can check your work as you go.
- Due Tuesday, March 25.
Worksheet: Forced Second-Order Linear Differential Equations. These problems will be collected and graded on Tuesday, March 25. Note: The left-hand side of the DE in #6 should be y'', NOT y'. You do not need to turn in #6--I apologize for the mistake.
If you would like some additional practice problems to work on, the following are good practice problems from your textbook. These problems will NOT be collected or graded.Suggested practice problems (not to be turned in or graded):
- 4.1: 1-41 odd
- 4.2: 1-13 odd
Homework 7 Solutions as a .pdf file
- Due Tuesday, April 1.
Worksheet: Forced Second-Order Linear Differential Equations. These problems will be collected and graded on Tuesday, April 1.
Homework 8 Solutions as a .pdf file
- Due Tuesday, April 8.
Worksheet: Sinusoidal Forcing
Homework 9 Solutions as a .pdf file
Maple file for Homework 9
- Due Thursday, April 10.
Worksheet: Higher Order Linear Differential Equations
Here are some additional practice problems for you to work on if you would like some more practice on solving higher order linear differential equations. The answers are included so that you can check your work as you go. These practice problems will not be collected or graded.
Homework 10 Solutions as a .pdf file
- Due Tuesday, April 22.
Worksheet: Series Solutions of Differential Equations, Part 1
Homework 11 Solutions as a .pdf file
- Practice problems on series solutions. The answers are included so that you can check your work as you go. These problems will not be collected or graded. For each problem, you should find the general recurrence relation, and then use the recurrence relation to try to write down the general solution of the DE. If you can't observe the general formula for the a_n, it's ok to just write down the first several terms of the series solution. In the posted solutions, don't worry about the y_1(x) and y_2(x). Just make sure that you are able to obtain the recurrence relation.
- Practice problems on Euler equations. The answers are included so that you can check your work as you go. These problems will not be collected or graded.
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