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Math - College, section 1, Fall 2019
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Zill - Diff. Equations with BV Prob. 9/e (Metric) (Homework)

James Finch

Math - College, section 1, Fall 2019

Instructor: Dr. Friendly

Current Score : 1 / 25

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

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

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Points

1	2	3	4	5	6	7	8	9	10
1/6	–/4	0/2	0/1	–/2	–/4	–/1	0/1	–/2	–/2

Total

1/25 (4.0%)

Instructions

Differential Equations with Boundary-Value Problems (Metric Version), 9th edition, by Dennis G. Zill and published by Cengage Learning, provides a thorough treatment of topics typically covered in a first course in Differential Equations, as well as an introduction to boundary-value problems and partial differential equations. This proven and easy-to-understand book speaks to beginning engineering and math students through a wealth of pedagogical aids, including an abundance of examples, explanations, "Remarks" boxes, definitions, and more. The WebAssign component for this text engages students with immediate feedback, a complete eBook, and a question bank of end-of-section exercises.

All questions feature Read It and Talk to a Tutor links.

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.

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. 1/6 points | Previous Answers ZillDiffEQ9M 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

³√5

$webMathematica generated answer key$

and

(2/π)y − sin(y) < 0 for y is in

π5

$webMathematica generated answer key$ ,

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⁄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.

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 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.

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

$webMathematica generated answer key$ unstable

$webMathematica generated answer key$ semi-stable

√4

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2. –/4 points ZillDiffEQ9M 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. 0/2 points | Previous Answers ZillDiffEQ9M 2.3.031. My Notes

Solve the given initial-value problem.

+ y = 2x + 1, y(1) = 9

y(x) =

r

$webMathematica generated answer key$

Give the largest interval I over which the solution is defined. (Enter your answer using interval notation.)

I =

t

$webMathematica generated answer key$

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4. 0/1 points | Previous Answers ZillDiffEQ9M 2.5.017. My Notes

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

= y(xy⁵ − 1)

$webMathematica generated answer key$

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5. –/2 points ZillDiffEQ9M 3.1.033. My Notes

An electromotive force

E(t) =

320,	0 ≤ t ≤ 20
0,		t > 20

is applied to an LR-series circuit in which the inductance is 40 henries and the resistance is 4 ohms. Find the current

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

i(t) =

,	0 ≤ t ≤ 20
,		t > 20

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6. –/4 points ZillDiffEQ9M 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 the origin, goes down and right becoming less steep, and exits the window almost horizontally above x = − r/k.

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.

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

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7. –/1 points ZillDiffEQ9M 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.]

∞

n = 0

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8. 0/1 points | Previous Answers ZillDiffEQ9M 8.2.001. My Notes

Find the general solution of the given system.

4x + 5y

10x + 9y

x(t), y(t)

$webMathematica generated answer key$

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9. –/2 points ZillDiffEQ9M A.B.004. My Notes

A =

1	5
8	11
10	12

and

B =

−5	9	−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 ZillDiffEQ9M A.B.048. My Notes

Consider the given matrix.

'		4
'		4

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 - Diff. Equations with BV Prob. 9/e (Metric) (Homework)

Current Score : 1 / 25

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

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

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