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Math - College, section 1, Fall 2019
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Zill - Differential Equations with Modeling 11/e (Homework)

James Finch

Math - College, section 1, Fall 2019

Instructor: Dr. Friendly

Current Score : 10 / 25

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
6/6	2/4	1/2	0/1	0/2	–/4	1/1	0/1	–/2	–/2

Total

10/25 (40.0%)

Instructions

A First Course in Differential Equations with Modeling Applications, 11th Edition written by Dennis Zill and published by Cengage Learning, strikes a balance between analytical, qualitative, and quantitative approaches to the study of differential equations. This proven resource speaks to students of varied majors through a wealth of pedagogical aids, including an abundance of examples, explanations, "Remarks" boxes, and definitions. It provides a thorough overview of the topics typically taught in a first course in differential equations written in a straightforward, readable, and helpful style. The WebAssign component for this title links to a complete eBook, engages students with videos and the ability to talk to a tutor, and supports the instructor with pre-made course packs.

Question 1 demonstrates interval grading, which can grade any canonically equivalent interval and enforces proper notation. Identical answer blanks handle zero, one, or multiple critical points.

Question 2 has the student find particular solutions through specified points. Part (a) accepts any solution in terms of an arbitrary or specific constant.

Question 3 contains a Watch It link to a video example that explains the solution method.

Question 4 features a randomized Bernoulli DE, where the solution can be entered implicitly or explicitly, and in terms of any arbitrary constant.

Question 5 shows an LR-series circuit application, where the student fills in each part of the piecewise-defined solution.

Question 6 features a mathematical model describing a real-world problem, where the student analyzes the end-behavior of the solution.

Question 7 illustrates how series are handled.

Question 8 utilizes special grading for the solution involving vectors and arbitrary constants. Also available is a Watch It video link.

Question 9 showcases expandable matrices, where the student determines the size of the matrix product, just as they would on paper.

Question 10 demonstrates how eigenvalues can be listed in any order, the number and size of the eigenvectors are defined by the student, and any correct eigenvector is accepted.

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.

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. 6/6 points | Previous Answers ZillDiffEQModAp11 2.1.031. My Notes

Consider the autonomous DE

dy/dx = (2/π)y − sin(y).

Determine the critical points of the equation. Discuss a way of obtaining a phase portrait of the equation. (Enter your answers using interval notation.)

Since

(2/π)y − sin(y) > 0 for y is in

(−π2,0)∪(π2,∞)

and

(2/π)y − sin(y) < 0 for y is in

(−∞,−π2) ∪(0,π2)

one obtains the following phase portrait.

A phase portrait is given. There are 4 arrows and 3 values on the phase line.
The arrow below the value −π points up.
The arrow between the values −π and 0 points down.
The arrow between the values 0 and π points up.
The arrow above the value π points down.

A phase portrait is given. There are 4 arrows and 3 values on the phase line.
The arrow below the value −π points down.
The arrow between the values −π and 0 points up.
The arrow between the values 0 and π points down.
The arrow above the value π points up.

A phase portrait is given. There are 4 arrows and 3 values on the phase line.
The arrow below the value −π⁄2 points down.
The arrow between the values −π⁄2 and 0 points up.
The arrow between the values 0 and π⁄2 points down.
The arrow above the value π⁄2 points up.

A phase portrait is given. There are 4 arrows and 3 values on the phase line.
The arrow below the value −π⁄2 points up.
The arrow between the values −π⁄2 and 0 points down.
The arrow between the values 0 and π⁄2 points up.
The arrow above the value π⁄2 points down.

Classify the critical points as asymptotically stable, unstable, or semi-stable. (List the critical points according to their stability. Enter your answers as a comma-separated list. If there are no critical points in a certain category, enter NONE.)

asymptotically stable

unstable

−π2,π2

semi-stable

NONE

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2. 2/4 points | Previous Answers ZillDiffEQModAp11 2.2.036. My Notes

Find a solution of

= y² − y

that passes through the indicated points.

(a)

(0, 1)

y =

(b)

(0, 0)

y =

(c)

y =

(d)

y =

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3. 1/2 points | Previous Answers ZillDiffEQModAp11 2.3.031. My Notes

Solve the given initial-value problem. Give the largest interval I over which the solution is defined.

+ y = 4x + 1, y(1) = 8

y =	2`x`2+`x`+5`x`
I =

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4. 0/1 points | Previous Answers ZillDiffEQModAp11 2.5.017. My Notes

Solve the given differential equation by using an appropriate substitution. The DE is a Bernoulli equation.

= y(xy⁶ − 1)

x+16+e6x+C

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5. 0/2 points | Previous Answers ZillDiffEQModAp11 3.1.033. My Notes

An electromotive force

E(t) =

350,	0 ≤ t ≤ 30
0,		t > 30

is applied to an LR-series circuit in which the inductance is 50 henries and the resistance is 5 ohms. Find the current

i(t) if i(0) = 0.

i(t) =

`B` ,	0 ≤ t ≤ 30
,		t > 30

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6. –/4 points ZillDiffEQModAp11 3.1.045. My Notes

A mathematical model for the rate at which a drug disseminates into the bloodstream is given by

= r − kx,

where r and k are positive constants. The function

x(t)

describes the concentration of the drug in the bloodstream at time t.

(a)

Since the DE is autonomous, use the phase portrait concept of Section 2.1 to find the limiting value of

x(t) as t → ∞.

lim t→∞ x(t) =

(b)

Solve the DE subject to

x(0) = 0.

x(t) =

Sketch the graph of

x(t)

and verify your prediction in part (a).

The t x-coordinate plane is given. The curve enters the window at x = − r/k on the negative x-axis, goes up and right becoming less steep, and exits the window almost horizontally below the t-axis.

The t x-coordinate plane is given. The curve enters the window at the origin, goes up and right becoming less steep, and exits the window almost horizontally below x = r/k.

The t x-coordinate plane is given. The curve enters the window at x = r/k on the positive x-axis, goes down and right becoming less steep, and exits the window almost horizontally above the t-axis.

The t x-coordinate plane is given. The curve enters the window at the origin, goes down and right becoming less steep, and exits the window almost horizontally above x = − r/k.

At what time is the concentration one-half this limiting value?

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7. 1/1 points | Previous Answers ZillDiffEQModAp11 6.1.017. My Notes

Use an appropriate series in (2) in Section 6.1 to find the Taylor series of the given function centered at the indicated value of a. Write your answer in summation notation.

sin x, a = 2π

[Hint: Use periodicity.]

∞	(−1)`n`(2`n`+1)!(`x`−2π)2`n`+1

n = 0

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8. 0/1 points | Previous Answers ZillDiffEQModAp11 8.2.001. My Notes

Find the general solution of the given system.

x + 2y

4x + 3y

x(t), y(t)

4t

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9. –/2 points ZillDiffEQModAp11 A.B.004. My Notes

A =

1	5
6	9
8	10

and

B =

−5	7	−4
1	−4	2

find

and

BA.

(If an answer does not exist, enter DNE into any cell of the matrix.)

(a)

(b)

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10. –/2 points ZillDiffEQModAp11 A.B.048. My Notes

Consider the given matrix.

'		8
'		8

Find the eigenvalues. (Enter your answers as a comma-separated list.)

λ =

Find the eigenvectors. (Enter your answers in order of the corresponding eigenvalues, from smallest eigenvalue to largest.)

K₁ =

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Zill - Differential Equations with Modeling 11/e (Homework)

Current Score : 10 / 25

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

Last Saved : n/a Saving... ()

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