/*! 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} Q13E 聽Find a general solution for th... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Q13E (page 332)

Find a general solution for the differential equation with x as the independent variable:

y(4)+4y''+4y=0

Short Answer

Expert verified

The general solution for the differential equation with x as the independent variable is

y(x)=c1cos(2x)+c2xcos(2x)+c3sin(2x)+c4xsin(2x)

Step by step solution

01

Auxiliary equation:

The auxiliary equation in this problem is r4+4r2+4=0. This can be factored as (r2+2)2=0. Therefore this equation has roots r=2i,鈭�2i,2i,鈭�2i, which we see are repeated and complex.

02

General solution:

The general solution to the given equation is given by

y(x)=c1cos(2x)+c2xcos(2x)+c3sin(2x)+c4xsin(2x)

Hence the final solution is y(x)=c1cos(2x)+c2xcos(2x)+c3sin(2x)+c4xsin(2x)

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

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.

xy'''-3y'+exy=x2-1y-2=1,鈥�鈥�y'-2=0,鈥�鈥�y''-2=2

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

y''-6y'+9y=sin2x+x

Given that {x,x-1,x4}is a fundamental solution set for the homogeneous equation corresponding to the equationx3y'''-x2y''-4xy'+4y=g(x),x>0,determine a formula involving integrals for a particular solution.

In Problems 1-6, use the method of variation of parameters to determine a particular solution to the given equation.

y'''-3y''+3y'-y=ex

In Problems 1-6, use the method of variation of parameters to determine a particular solution to the given equation.

y'''+y'=tanx
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Geometry

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Statistics

Read Explanation

Mechanics 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.