WebAssign is not supported for this browser version. Some features or content might not work. System requirements

WebAssign

Welcome, demo@demo

(sign out)

Saturday, March 29, 2025 02:22 EDT

Home My Assignments Grades Communication Calendar My eBooks

Noonburg - Ordinary Differential Equations 2/e (Homework)

James Finch

Math - College, section 1, Fall 2019

Instructor: Dr. Friendly

Current Score : 14 / 18

Due : Sunday, January 27, 2030 00:00 EST

Last Saved : n/a Saving...  ()

Ask Your Teacher Print Assignment
Question
Points
1 2 3 4 5 6
3/3 0/1 1/1 4/4 4/4 2/5
Total
14/18 (77.8%)

  • Instructions

    Ordinary Differential Equations: From Calculus to Dynamical Systems: Second Edition, published by the Mathematical Association of America, is a new edition of Virginia Noonburg's bestselling text. A thoroughly modern textbook for the sophomore-level differential equations course, the book includes two new chapters on partial differential equations, making it usable for a two-semester sequence. The examples and exercises emphasize modeling not only in engineering and physics but also in applied mathematics and biology. There is an early introduction to numerical methods and, throughout, a strong emphasis on the qualitative viewpoint of dynamical systems. Bifurcations and analysis of parameter variation is a persistent theme.

    Presuming previous exposure to only two semesters of calculus, necessary linear algebra is developed as needed. The book's clear and inviting exposition makes it ideal for use in a flipped-classroom pedagogical approach or for self-study for an advanced undergraduate or beginning graduate student. It includes exercises, examples, and extensive student projects taken from the current mathematical and scientific literature. The WebAssign component of this text features immediate student feedback and question links to an eBook.

    Question 1 first steps the student through proving a function. Then, it has the student enter an interval using interval notation.

    Question 2 uses differential equation grading to test the validity of the answer. This question accepts any correct form of the answer and runs student's responses through a series of tests to ensure the assumptions and requirements of the question are met.

    Question 3 asks the student to solve a randomized initial-value problem; any correct form of the equation is accepted.

    Question 4 asks the student to explain the behavior of the slope field that is given with a series of fill-in-the-blank answers. For the first blank, try entering INFINITY and "∞" to see that both are accepted.

    Question 5 uses special grading that allows the student to enter arbitrary solutions for the source, sinks, and nodes. However, no equilibrium points exist for the node category, so an answer of NONE is expected.

    Question 6 includes vector grading which allows component form as well as i , j, k (or i, j, k) form of the vector. This question also asks the student to sketch the tangent vectors.

Assignment Submission

For this assignment, you submit answers by question parts. The number of submissions remaining for each question part only changes if you submit or change the answer.

Assignment Scoring

Your last submission is used for your score.

1. 3/3 points  |  Previous Answers NoonburgDiffEQ2 1.1.010. My Notes
Question Part
Points
Submissions Used
1 2 3
1/1 1/1 1/1
3/5 3/5 1/5
Total
3/3
 
For the equation below, show that the given function is a solution. (Enter your answers in terms of t.)
x'' + 9x = 0,
    
x(t) = sin(3t) + cos(3t)
Since
x''(t) =
−9sin(3t)−9cos(3t)
Correct: Your answer is correct.
and
9x(t) =
9sin(3t)+9cos(3t)
Correct: Your answer is correct. ,
 it is apparent that
x(t) = sin(3t) + cos(3t)
 is a solution to the given equation.
Determine the largest interval or intervals of the independent variable over which the solution is defined, and satisfies the equation. (Enter your answer using interval notation.)
(−∞, ∞)
Correct: Your answer is correct.
Your work in question(s) will also be submitted or saved.
Viewing Saved Work Revert to Last Response
2. 0/1 points  |  Previous Answers NoonburgDiffEQ2 2.1.006. My Notes
Question Part
Points
Submissions Used
1
0/1
5/5
Total
0/1
 
Put the equation into the form
x'(t) = g(t)h(x),
 and solve by the method of separation of variables.
x' = 
t
x
$$x 2=t2
Incorrect: Your answer is incorrect.
Viewing Saved Work Revert to Last Response
3. 1/1 points  |  Previous Answers NoonburgDiffEQ2 2.1.016. My Notes
Question Part
Points
Submissions Used
1
1/1
2/5
Total
1/1
 
Solve the initial-value problem.
y' = ty,
    
y(0) = 7
y=7(t22​)
Your work in question(s) will also be submitted or saved.
Viewing Saved Work Revert to Last Response
4. 4/4 points  |  Previous Answers NoonburgDiffEQ2 2.2.012. My Notes
Question Part
Points
Submissions Used
1 2 3 4
1/1 1/1 1/1 1/1
1/5 2/5 2/5 1/5
Total
4/4
 
You are given a differential equation. The corresponding slope field has also been drawn. Sketch enough solution curves in the slope field to be able to describe the behavior of the family of solutions in the entire
(t, x)
-plane. As part of your description, explain how the long-term behavior depends on the initial condition
x(0).
 Be as specific as possible.
x' = 
t
x
WebAssign Plot
If x(0) is positive, the solution tends to
∞
Correct: Your answer is correct. as t approaches ∞. It is also clear that solutions with
x(0) > 0
remain above the line
x=t
. For
x(0) < 0,
the solution stays below the line
x=−t
and tends to
−∞
Correct: Your answer is correct. as t approaches ∞.
Your work in question(s) will also be submitted or saved.
Viewing Saved Work Revert to Last Response
5. 4/4 points  |  Previous Answers NoonburgDiffEQ2 2.7.006. My Notes
Question Part
Points
Submissions Used
1 2 3 4
1/1 1/1 1/1 1/1
1/5 5/5 5/5 2/5
Total
4/4
 
Draw a phase line for the autonomous differential equation. Hint: plot
f(x) = sin(x)
 to determine the direction of the arrows. (Draw the phase line only on the interval
− 
3π
2
, 
5π
2
.
x' = sin(x)

Correct: Your answer is correct.
Classify each equilibrium point as a sink, source, or node. (Include points not in the graph above. Use n to represent any arbitrary integer. Enter your answers as comma-separated lists. If there are no equilibrium points in a certain category, enter NONE.)
source(s)
$$2Nπ
Correct: Your answer is correct. sink(s)
$$2aπ−π
Correct: Your answer is correct. node(s)
none
Correct: Your answer is correct.
Your work in question(s) will also be submitted or saved.
Viewing Saved Work Revert to Last Response
6. 2/5 points  |  Previous Answers NoonburgDiffEQ2 3.7.002. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5
1/1 0/1 0/1 0/1 1/1
1/5 1/5 1/5 1/5 1/5
Total
2/5
 
Write the given equation in the form
x'' = F(x, x').
 (Use the variable xp to represent x'.)
x'' + 0.8x' + 10 sin(x) = 0
F(x, x')
=
−0.8xp−10sin(x)
Correct: Your answer is correct.
Compute the tangent vectors
(x, x')
 at the points
(−2.3, 0),
(2.3, −3),
 and
(−3, 4).
 (Round all values to three decimal places.)
T(x, x') = x'  i  + F(x, x') j 
T(−2.3, 0)
=
2
Incorrect: Your answer is incorrect.
T(2.3, −3)
=
2
Incorrect: Your answer is incorrect.
T(−3, 4)
=
2
Incorrect: Your answer is incorrect.
Sketch the tangent vectors in the given phase plane. Note: to draw the tangent vector
T = A i  + B j 
 at the point
(x, x'),
 draw a short line from the point
(x, x')
 toward the point
(x + A, x' + B).

Correct: Your answer is correct.
Your work in question(s) will also be submitted or saved.
Viewing Saved Work Revert to Last Response
Home My Assignments