/*! 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} Q24 E In Problems 23-28, determine whe... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Q24 E (page 14)

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

dydt-ty=sin2t,y(蟺)=5

Short Answer

Expert verified

The hypotheses of Theorem 1 are satisfied.

It follows from the theorem that the given initial value problem has a unique solution.

Step by step solution

01

Finding the partial derivative of the given relation concerning y.

Here, ft,y=sin2t+tyand鈭�f鈭�y=t.

02

Determining whether Theorem 1 implies the existence of a unique solution or not.

Now from Step 1, we find that both of the functionsft,yand鈭�f鈭�yare continuous in any rectangle containing the point 蟺,5, so the hypotheses of Theorem 1 are satisfied. It then follows from the theorem that the given initial value problem has a unique solution in an interval aboutt=蟺 of the form role="math" localid="1664002842140" 蟺-未,蟺+未, where is some positive number.

Hence, Theorem 1 implies that the given initial value problem has a unique 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

Decide whether the statement made is True or False. The function x(t)=t-3sint+4t-3 is a solution to t3dxdt=cost-3t2x.

In Problems 14鈥�24, you will need a computer and a programmed version of the vectorized classical fourth-order Runge鈥揔utta algorithm. (At the instructor鈥檚 discretion, other algorithms may be used.)鈥�

Using the vectorized Runge鈥揔utta algorithm, approximate the solution to the initial value problem y''=t2+y2;y(0)=1,y'(0)=0at t=1. Starting with h=1, continue halving the step size until two successive approximations of both y1andy'1differ by at most 0.1.

Decide whether the statement made is True or False. The relation siny+ey=x6-x2+x+1 is an implicit solution to dydx=6x5-2x+1cosy+ey.

In Problems 9鈥�20, determine whether the equation is exact.

If it is, then solve it.

(2xy+3)dx+(x2-1)dy=0

Using the Runge鈥揔utta algorithm for systems with h = 0.05, approximate the solution to the initial value problem y'''+y''+y2=t;y(0)=1,y'(0)=0,y''(0)=1 at t=1.
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

Read Explanation

Mechanics Maths

Read Explanation

Decision 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.