/*! 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} Q. 3 What is the difference between a... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Q. 3 (page 569)

What is the difference between a solution of a differential equation and a solution of an initial-value problem?

Short Answer

Expert verified

The differential equation and the initial condition are both satisfied by the only solution, which is y=x2.

Step by step solution

01

Given information

A solution to an initial value problem is the one and only function that solves both the differential equation and the initial value problem, whereas a solution to a differential equation is one of potentially many functions that make the differential equation true.

02

Calculation

Take the differential equation dydx=2x, for instance, whose solution is y=x2+C. Therefore, one of the solutions that satisfies the differential equation is y=x2+3. The initial-value problem, however, isdydx=2x;y(0)=0. The differential equation and the initial condition are both satisfied by the only solution, which is y=x2.

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

Use antidifferentiation and/or separation of variables to solve each of the differential equations in Exercises 19鈥�28. Your answers will involve unsolved constants.

28.dydx=x2e-y

Approximate the arc length of f (x) on [a, b], using n line segments and the distance formula. Include a sketch of f (x) and the line segments .

fx=x3,a,b=-2,2,n=4

The area of the surface obtained by revolving the curve

fx=sin蟺xaround the x-axis on-1,1.

Use antidifferentiation and/or separation of variables to solve each of the initial-value problems in Exercises 29鈥�52.

34.dydx=1y,y0=3

Each of the definite integrals in Exercises 19鈥�24 represents the volume of a solid of revolution obtained by rotating a region around either the x- or y-axis. Find this region.

蟺鈭�15y-122dy
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Logic and Functions

Read Explanation

Pure Maths

Read Explanation

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Applied Mathematics

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.