/*! 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} Q3E Determine the largest interval (... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Q3E (page 326)

Determine the largest interval (a, b) for which Theorem 1 guarantees the existence of a unique solution on (a, b) to the given initial value problem.

y'''-y''+x-1y=tanxy5=y'5=y''5=1

Short Answer

Expert verified

Hence, the largest interval for the existence of a unique solution to the given initial value problem is:

3蟺2,鈥�鈥�5蟺2

Step by step solution

01

Solve the given equation

The given equation isy'''-y''+x-1y=tanx.

Compare with the standard form of a linear differential equation,

y'''+pxy''+qxy'+rxy=sx

We have,px=-1,鈥�鈥�rx=x-1,鈥�鈥�sx=tanx

02

Step 2:Check the continuity

rx=x-1is continuous for allx-1<0

That is r is continuousx<1.

And

sx=tanxis continuous in2n-1蟺2,鈥�鈥�2n+1蟺2

For n = 2,

sx=tanxis continuous in3蟺2,鈥�鈥�5蟺2

03

Step 3:The largest interval (a, b)

Now p and r continuous for all x鈭�-鈭�,鈥�鈥�1.

And s is continuous in3蟺2,鈥�鈥�5蟺2

The initial condition is defined atx0=5

And5鈭�3蟺2,鈥�鈥�5蟺2

Hence, the largest interval for the existence of a unique solution on (a, b) to the given initial value problem is:3蟺2,鈥�鈥�5蟺2

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

find a general solution to the given equation.

y'''+4y''+y'-26y=e-3xsin2x+x

find a general solution to the given equation.

y'''+y''-2y=xex+1

use the annihilator method to determinethe form of a particular solution for the given equation.

y''+2y'+y=x2-x+1

Find a general solution for the given linear system using the elimination method of Section 5.2.

d2xdt2鈭�x+5y=02x+d2ydt2+2y=0

find a differential operator that annihilates the given function.

e5x
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Decision Maths

Read Explanation

Logic and Functions

Read Explanation

Applied Mathematics

Read Explanation

Calculus

Read Explanation

Probability and Statistics

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.