/*! 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} Q56E In Problems 7鈥�12 match each of... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 12: Q56E (page 527)

In Problems 7鈥�12 match each of the given differential equations with one or more of these solutions:

(a) \(y = 0\), (b) \(y = 2\), (c) \(y = 2x\), (d) \(y = 2{x^2}\)

\(y' = 2\)

Short Answer

Expert verified

The solution is \({\rm{y = 2x}}\).

Step by step solution

01

Check \(y = 0\) if is a solution.

Put\({\rm{y = 0}}\).

\(\begin{array}{c}(0)' = 2\\0 = 2\\0 \ne 2\end{array}\)

Hence, it is not a solution.

02

Check \(y = 2\) if is a solution.

Put\({\rm{y = 2}}\).

\(\begin{array}{c}(2)' = 2\\0 = 2\\0 \ne 2\end{array}\)

Hence, it is not a solution.

03

Check \(y = 2x\) if is a solution.

Put\({\rm{y = 2x}}\).

\(\begin{array}{c}(2x)' = 2\\2x = 2\\2 = 2\end{array}\)

Hence, it is a solution.

04

Check \(y = 2{x^2}\) if is a solution.

Put \({\rm{y = 2}}{{\rm{x}}^2}\).

\(\begin{array}{c}(2{x^2})' = 2\\4x = 2\\4x \ne 2\end{array}\)

Hence, it is not a solution.

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

In Problems 25鈥�28 use (12) to verify that the indicated function is a solution of the given differential equation. Assume an appropriate interval I of definition of each solution.

\({x^2}\frac{{dy}}{{dx}} + xy = 10sinx;y = \frac{5}{x} + \frac{{10}}{x}\int_1^x {\frac{{sint}}{t}} dt\)

In Problems 27鈥�30 use (12) of Section 1.1 to verify that the indicated function is a solution of the given differential equation. Assume an appropriate interval I of definition of each solution.

\(\frac{{dy}}{{dx}} - 2xy = {e^{{x_z}}}; y = {e^{{x^2}}}\int_0^x {{e^{t - {t^2}}}} dt\)

In Problems \(11 - 14\) verify that the indicated function is an explicit solution of the given differential equation. Assume an appropriate interval I of definition for each solution.

\(\frac{{dy}}{{dt}} + 20y = 24; y = \frac{6}{5} - \frac{6}{5}{e^{ - 20t}}\).

(a) Verify that the one-parameter family \({y^2} - 2y = {x^2} - x + c\) is an implicit solution of the differential equation \((2y - 2)y' = 2x - 1\).

(b) Find a member of the one-parameter family in part (a) that satisfies the initial condition \(y(0) = 1\).

(c) Use your result in part (b) to and an explicit function \(y = \phi (x)\) that satisfies \(y(0) = 1\). Give the domain of the function \(\phi \). Is \(y = \phi (x)\) a solution of the initial-value problem? If so, give its interval \(I\) of definition; if not, explain.

(a) Give the domain of the function \(y = {x^{{\textstyle{2 \over 3}}}}\).

(b) Give the largest interval I of definition over which \(y = {x^{{\textstyle{2 \over 3}}}}\) is a solution of the differential equation \(3xy' - 2y = 0\).
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Calculus

Read Explanation

Logic and Functions

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Geometry

Read Explanation

Mechanics Maths

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.