/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q13E In Problems 9鈥�20, determine wh... [FREE SOLUTION] | 91影视

91影视

Find study content
Learning Materials

Discover learning materials by subject, university or textbook.

Explanations

Textbooks
All Subjects

Anthropology

Archaeology

Architecture

Art and Design

Bengali

Biology

Business Studies

Greek

Chemistry

Chinese

Combined Science

Computer Science

Economics

Engineering

English

English Literature

Environmental Science

French

Geography

German

History

Hospitality and Tourism

Human Geography

Italian

Japanese

Law

Macroeconomics

Marketing

Math

Media Studies

Medicine

Microeconomics

Music

Nursing

Nutrition and Food Science

Physics

Polish

Politics

Psychology

Religious Studies

Sociology

Spanish

Sports Sciences

Translation

All Subjects

Biology

Business Studies

Chemistry

Combined Science

Computer Science

Economics

English

Environmental Science

Geography

History

Math

Physics

Psychology

Sociology
Features
Features

Discover all of these amazing features with a free account.

Flashcards

91影视 AI

Notes

Study Plans

Study Sets
What鈥檚 new?

Flashcards
Study your flashcards with three learning modes.

Study Sets
All of your learning materials stored in one place.

Notes
Create and edit notes or documents.

Study Plans
Organise your studies and prepare for exams.
91影视
Discover

All the hacks around your studies and career - in one place.

Find a degree

Magazine
Featured

Magazine
Trusted advice for anyone who wants to ace their studies & career.

The largest student job board with the most exciting opportunities.

Verified student deals from top brands.

Discover our mobile app to take your studies anywhere.

Learning Materials

Features

Discover

Fundamentals Of Differential Equations And Boundary Value Problems

R. Kent Nagle, Edward B. Saff, Arthur David Snider

$Math Studyset 91影视 Explanations$ Math

9th Edition 路 616 pages

ISBN: 9780321977069

Chapter 1: Q13E (page 1)

In Problems 9鈥�20, determine whether the equation is exact.
If it is, then solve it.
$e^{t} (y - t) dt + ({1 +e}^{t}) dy = 0$

Short Answer

Expert verified

The solution is $y = \frac{(t - 1) e^{t} + C}{1 + e^{t}}$ .

Step by step solution

01

Evaluate whether the equation is exact

Here $e^{t} (y - t) dt + ({1 +e}^{t}) dy = 0$

The condition for exact is $\frac{鈭� M}{鈭� y} = \frac{鈭� N}{鈭� t}$ .

$M (t, y) = e^{t} (y - t) N (t, y) = (1 + e^{t})$

$\frac{鈭� M}{鈭� y} = e^{t} = \frac{鈭� N}{鈭� t}$

This equation is exact.

02

Find the value of F (x, t)

Here

$M (t, y) = e^{t} (y - t) F (t, y) = 鈭� M (t, y) dt + g (y) = 鈭� e^{t} (y - t) dt + g (y) = e^{t} y - e^{t} t + e^{t} + g (y)$

03

Determine the value of g(y)

$\frac{鈭� F}{鈭� y} (t, y) = N (t, y) e^{t} + g' (y) = 1 + e^{t} g' (y) = 1 g (y) = y + C_{1}$

Now ${F(t,y) =e}^{t} {y -e}^{t} {t +e}^{t} {+ y +C}_{1}$

The general solution of the differential equation is $y = \frac{(t - 1) e^{t} + C}{1 + e^{t}}$

Hence the solution isrole="math" localid="1664172391787" $y = \frac{(t - 1) e^{t} + C}{1 + e^{t}}$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Show that $蠒 (x) = {Ce}^{3 x} + 1$ is a solution tolocalid="1663944867164" $\frac{d y}{d x} - 3 y = - 3$ for any choice of the constant C. Thus, ${Ce}^{3 x} + 1$ is a one-parameter family of solutions to the differential equation. Graph several of the solution curves using the same coordinate axes.

In Problems 23-28, determine whether Theorem 1 implies that the given initial value problem has a unique solution.

$\frac{dy}{dx} = 3 x - \sqrt[3]{y - 1}, y (2) = 1$

Verify that $蠒 (x) = \frac{2}{(1 - {ce}^{x})},$ where c is an arbitrary constant, it is a one-parameter family of solutions to $\frac{dy}{dx} = \frac{y (y - 2)}{2}$ . Graph the solution curves corresponding to $c = 0, 卤 1, 卤 2$ using the same coordinate axes.

Verify that $x^{2} + {cy}^{2} = 1,$ where c is an arbitrary non-zero constant, is a one-parameter family of implicit solutions to $\frac{dy}{dx} = \frac{xy}{x^{2} - 1}$ and graph several of the solution curves using the same coordinate axes.

(a) For the initial value problem (12) of Example 9. Show that $蠒_{1} (x) = 0$ and $蠒_{2} (x) = {(x - 2)}^{3}$ are solutions. Hence, this initial value problem has multiple solutions. (See also Project G in Chapter 2.)

(b) Does the initial value problem $y' = 3 y^{\frac{2}{3}},$ $y (0) = 10^{- 7}$ have a unique solution in a neighbourhood of $x = 0$ ?

See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Decision Maths

Read Explanation

Logic and Functions

Read Explanation

Probability and Statistics

Read Explanation

Calculus

Read Explanation

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.