/*! 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. 38 Use antidifferentiation and/or s... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Q. 38 (page 570)

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

dydx=4y,y(1)=1

Short Answer

Expert verified

The solution of the initial - value problem dydx=4y,y(1)=1isy(x)=x2

Step by step solution

01

Step 1. Given information

The given initial value problemdydx=4y,y(1)=1............(1)

02

Step 2. Use antidifferentiation and/or separation of variables to solve each of the initial-value 

Note that the differential equation in (1) does not contain the independent variable at all, so technically the variables have already been separated. Hence, the differential equation can be solved by antidifferentiating. Thus, the solution of the differential equation involved in the initialvalue problem is given by

鈭�12ydy=鈭�dxy=x+c

Now, use the given initial condition y(1)=1, that is take x=1,y=1 in the above result and evaluate the constant C.

1=1+CC=0

Substitute this value of the constantCin the solution of the differential equation to get
y=xy=x2
Hence, the solution of the initial - value problem dydx=4y,y(1)=1isy(x)=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 initial-value problems in Exercises 29鈥�52.

29. dydx=3y,y0=4

For each pair of definite integrals in exercise 13-18 decide which if either is larger without computing the integrals

蟺鈭�02x4dxand蟺鈭�02(x4-16)dx

Consider the region between the graph of fx=x-2and the x-axis on [2, 5]. For each line of rotation given in Exercises 35鈥�40, use definite integrals to find the volume of the resulting solid.

Explain how equality dydxxk,yk=螖yk螖xis relevant to Euler鈥檚 method.

Write the volume of the two solids of revolution that follow in terms of definite integrals that represent accumulations of disks and/or washers. Do not compute the integrals.
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Geometry

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.