/*! 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} Q4.3-20E Find a general solution.y'''-y''... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Q4.3-20E (page 172)

Find a general solution.y'''-y''+2y=0

Short Answer

Expert verified

The general solution of the given equation y'''-y''+2y=0isy(t)=C1e-t+C2etcos(t)+C3etsin(t).

Step by step solution

01

Using rational root theorem.

First, you need to find the auxiliary equation and solve it. One has r3-r2+2=0.

The first divisor of role="math" localid="1654074445353" 2is 1 if 1will be one solution of the equation and (r-1) will be a factor.

That doesn't happen, but next, you can try with -1 so thatr+1 would be a factor.

02

Finding factor

Now you can divide r3-r2+2by r+1to get r2-2r+2.

Therefore, the equation can be factored as (r+1)(r2-2r+2)=0

Since r2-2r+2=0

role="math" localid="1654074733241" r=2卤22-4脳1脳22r=1卤i

03

Finding roots.

The roots of the auxiliary equation are r=-1,r=1+iand r=1-i

Thus, the general solution of the differential equation is:

y(t)=C1e-t+C2etcos(t)+C3etsin(t)

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 particular solution to the differential equation.

y''(x)+y(x)=4xcosx

Find the solution to the initial value problem.

y''(x)-y'(x)-2y(x)=cosx-sin2x;鈥夆赌夆赌夆赌夆赌�y(0)=-720,鈥夆赌夆赌夆赌�y'(0)=15

Find a particular solution to the given higher-order equation.

y'''-2y''-y'+2y=2t2+4t-9

Find a general solution y''+4y'+8y=0

Decide whether the method of undetermined coefficients together with superposition can be applied to find a particular solution of the given equation. Do not solve the equation.

y''+ety'+y=7+3t
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Discrete Mathematics

Read Explanation

Calculus

Read Explanation

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Logic and Functions

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.