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McOwen - Worldwide Diff Eq with Linear Alg 1/e (Homework)

James Finch

Math - College, section 1, Fall 2019

Instructor: Dr. Friendly

Current Score : 13 / 29

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

Last Saved : n/a Saving...  ()

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Question
Points
1 2 3 4 5 6 7 8 9 10 11
2/2 4/4 0/1 –/1 6/7 –/1 1/4 –/1 –/1 –/1 –/6
Total
13/29 (44.8%)

  • Instructions

    Worldwide Differential Equations with Linear Algebra, 1st edition by Robert McOwen, published by Worldwide Center of Mathematics, is designed for a one-semester undergraduate course in ordinary differential equations and linear algebra. This text adopts a concise writing style and careful selection of topics to keep the book shorter than many others on this subject. The WebAssign component to this textbook provides students with immediate feedback, videos of worked problems, and a searchable eBook.

    Questions 6 and 10 have a video of the worked problem.

    Question 3 uses differential equation grading to test the validity of the answer. 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 5 walks the student through how to verify the given functions satisfy the given second-order equation.

    Question 6 uses differential equation grading to test the validity of the answer. 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.

    Questions 7 and 8 use the matrix tool, which allows student to define the size of the resulting matrix.

    Question 9 demonstrates grading for solutions of dependent systems. Try inputting different forms of the correct answer!

    Question 11 showcases grading for bases, which accepts any correct eigenvector. Try multiplying by a constant!

    View the complete list of WebAssign questions available for this textbook This demo assignment allows many submissions and allows you to try another version of the same question for practice wherever the problem has randomized values.

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1. 2/2 points  |  Previous Answers WWCMDiffEQLinAlg1 1.2.001. My Notes
Question Part
Points
Submissions Used
1 2
1/1 1/1
1/50 2/50
Total
2/2
 
Sketch the slope field and some solution curves for the following equations.
(a)    
dy
dx
 = x − y


(b)    
dy
dx
 = y − sin(x)

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2. 4/4 points  |  Previous Answers WWCMDiffEQLinAlg1 1.2.003b. My Notes
Question Part
Points
Submissions Used
1 2 3 4
1/1 1/1 1/1 1/1
2/50 2/50 2/50 2/50
Total
4/4
 
Find all equilibrium solutions for the following autonomous equation, and determine the stability of each equilibrium. (Enter your answers from smallest to largest.)
dy
dt
 = y2 − y3
y = Correct: Your answer is correct. seenKey

0
which is Correct: Your answer is correct. seenKey

semistable
y = Correct: Your answer is correct. seenKey

1
which is Correct: Your answer is correct. seenKey

stable

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3. 0/1 points  |  Previous Answers WWCMDiffEQLinAlg1 1.4.001b. My Notes
Question Part
Points
Submissions Used
1
0/1
1/50
Total
0/1
 
Find the general solution for the following linear differential equation. (Prime
'
 denotes
d/dx.)
y' + 2y = xe−2x
y(x) =
e−2xxy2
Incorrect: Your answer is incorrect. webMathematica generated answer key

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4. –/1 points WWCMDiffEQLinAlg1 1.4.007. My Notes
Question Part
Points
Submissions Used
1
–/1
0/50
Total
–/1
 
The rate of change of the temperature T(t) of a body is still governed by
dT
dt
 = −k(T − A),    T(0) = T0,
when the ambient temperature A(t) varies with time. Suppose the body is known to have
k = 0.2
 and initially is at 23°C; suppose also that
A(t) = 20e−t.
 Find the temperature T(t).
T(t) =

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5. 6/7 points  |  Previous Answers WWCMDiffEQLinAlg1 2.2.003. My Notes
Question Part
Points
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1 2 3 4 5 6 7
1/1 1/1 1/1 1/1 1/1 1/1 0/1
1/50 1/50 1/50 2/50 2/50 2/50 1/50
Total
6/7
 
Consider the following.
y'' − 2y' + y = 0;
y1(x) = ex,
y2(x) = xex.
I.C. y(0) = 5,
y'(0) = 7
(a) Verify that y1 and y2 satisfy the given second-order equation.
y1 = ex,
y1' =
ex
Correct: Your answer is correct. webMathematica generated answer key ,
y1'' =
ex
Correct: Your answer is correct. webMathematica generated answer key .
 Therefore,
y1'' − 2y1' + y1 =
0
Correct: Your answer is correct. webMathematica generated answer key .
y2 = xex,
y2' =
exx+ex
Correct: Your answer is correct. webMathematica generated answer key ,
y2'' =
exx+2ex
Correct: Your answer is correct. webMathematica generated answer key .
 Therefore,
y2'' − 2y2' + y2 =
0
Correct: Your answer is correct. webMathematica generated answer key .

(b) Find the solution satisfying the given initial conditions (I.C.).
y(x) =
7ex+4
Incorrect: Your answer is incorrect. webMathematica generated answer key

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6. –/1 points WWCMDiffEQLinAlg1 2.3.002c. My Notes
Question Part
Points
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1
–/1
0/50
Total
–/1
 
Find the general solution.
y'' + 4y' + 4y = 0
y(x) =

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7. 1/4 points  |  Previous Answers WWCMDiffEQLinAlg1 4.1.002. My Notes
Question Part
Points
Submissions Used
1 2 3 4
1/1 –/1 –/1 –/1
1/50 0/50 0/50 0/50
Total
1/4
 
For the following matrices A and B calculate 2A, 3B,
A + B,
 and
A − 2B.
A = 
10−1
145
,    B = 
014
410
2A =

Correct: Your answer is correct. seenKey

[2,0,-2;2,8,10]
3B =

A + B =

A − 2B =

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8. –/1 points WWCMDiffEQLinAlg1 4.2.002c. My Notes
Question Part
Points
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1
–/1
0/50
Total
–/1
 
Use Gaussian elimination to put the following matrix into row-echelon form.
210−1
0010
1297

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9. –/1 points WWCMDiffEQLinAlg1 4.2.003b. My Notes
Question Part
Points
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1
–/1
0/50
Total
–/1
 
For the following linear system, put the augmented coefficient matrix into row-echelon form, and then use back substitution to find all solutions. (If the system is inconsistent, enter INCONSISTENT. If there are an infinite number of solutions use t as your parameter.)
3x1 − 6x2 − 2x3 = 16
2x1 − 4x2 + x3 = 27
x1 − 2x2 − 2x3 = −4
(x1, x2, x3) = 

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10. –/1 points WWCMDiffEQLinAlg1 4.5.002a. My Notes
Question Part
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1
–/1
0/50
Total
–/1
 
Find the values of k for which the system has a nontrivial solution. (Enter your answers as a comma-separated list.)
x1 + kx2 = 0
kx1 + 49x2 = 0
k =

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11. –/6 points WWCMDiffEQLinAlg1 6.1.002c. My Notes
Question Part
Points
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1 2 3 4 5 6
–/1 –/1 –/1 –/1 –/1 –/1
0/50 0/50 0/50 0/50 0/50 0/50
Total
–/6
 
The following matrix has (some) complex eigenvalues. Find all eigenvalues and associated eigenvectors. (Order eigenvalues from smallest to largest real part, then by imaginary part.)
100
00−4
040
λ1 =
    


has eigenvector(s)   



λ2 =
    


has eigenvector(s)   



λ3 =
    


has eigenvector(s)   



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