/*! 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. 52 Use antidifferentiation and/or s... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Q. 52 (page 570)

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

dydx=y+1x2+1,y(0)=1

Short Answer

Expert verified

On solving, we gety(x)=2etan-1x-1

Step by step solution

01

Step 1. Given information

Given expressiondydx=y+1x2+1,y(0)=1

02

Using the variable separable method

Calculating, we get

鈭�1y+1dy=鈭�1x2+1dxln|y+1|=tan-1x+Cy+1=etan-x+cy=-1+Aetan-1x

03

Substitute x=0y=1 and calculate

Calculating, we get

1=-1+AA=2y(x)=2etan-1x-1

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

Consider the region between the graph of f(x)=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.

find an equation that gives y as an implicit function of x. Then draw the continuous curve that satisfies this differential equation and passes through the point (2, 0).

dydx=xy

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

dydx=xy+x+y+1,y(0)=c

The area of the surface obtained by revolving the curve

fx=sin蟺xaround the x-axis on-1,1.

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
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Mechanics Maths

Read Explanation

Logic and Functions

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.