Skip to main content

Math Algebra Differential Equations and Linear Algebra (4th Edition)

For Problems 33-37, solve the given initial value problem. ( D 2 + D − 2 ) y = 4 cos x − 2 sin x , y ( 0 ) = − 1 , y ′ ( 0 ) = 4

For Problems 33-37, solve the given initial value problem. ( D 2 + D − 2 ) y = 4 cos x − 2 sin x , y ( 0 ) = − 1 , y ′ ( 0 ) = 4

Solution Summary: The author explains how to determine the solution of the given initial value problem.

Differential Equations and Linear Algebra (4th Edition)

Differential Equations and Linear Algebra (4th Edition)

4th Edition

ISBN: 9780321964670

Author: Stephen W. Goode, Scott A. Annin

Publisher: PEARSON

See similar textbooks

Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

Videos

Textbook Question

Chapter 8.3, Problem 36P

For Problems 33-37, solve the given initial value problem.

( D 2 + D − 2 ) y = 4 cos x − 2 sin x , y ( 0 ) = − 1 , y ′ ( 0 ) = 4

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

Blurred answer

Chapter 8.3, Problem 35P

Chapter 8.3, Problem 37P

Students have asked these similar questions

Answer the questions

Solve questions by Course Name (Ordinary Differential Equations II 2)

please Solve questions by Course Name( Ordinary Differential Equations II 2)

Chapter 8 Solutions

Differential Equations and Linear Algebra (4th Edition)

Ch. 8.1 - True-False Review For Questions a-j, decide if the...Ch. 8.1 - True-False Review For Questions a-j, decide if the...Ch. 8.1 - True-False Review For Questions a-j, decide if the...Ch. 8.1 - True-False Review For Questions a-j, decide if the...Ch. 8.1 - Prob. 5TFR Ch. 8.1 - Prob. 6TFR Ch. 8.1 - True-False Review For Questions a-j, decide if the...Ch. 8.1 - Prob. 8TFR Ch. 8.1 - Prob. 9TFR Ch. 8.1 - True-False Review For Questions a-j, decide if the...

Ch. 8.1 - Problems For problem 1-4, find Ly for the given...Ch. 8.1 - Problems For problem 1-4, find Ly for the given...Ch. 8.1 - Problems For problem 1-4, find Ly for the given...Ch. 8.1 - Problems For problem 1-4, find Ly for the given...Ch. 8.1 - Problems For problem 5-9, verify that given...Ch. 8.1 - Prob. 6P Ch. 8.1 - Problems For problem 5-9, verify that given...Ch. 8.1 - Problems For problem 5-9, verify that given...Ch. 8.1 - Prob. 9P Ch. 8.1 - Problems For problem 10-13, compute Ker(L). L=D3x2 Ch. 8.1 - For Problems 10-13, compute Ker(L). L=D2+1 Ch. 8.1 - For Problem 10-13, compute ker(L). L=D2+2D15Hint:...Ch. 8.1 - For Problems 10-13, compute Ker(L). L=x2D+x.Ch. 8.1 - Problems For problems 14-15, find L1L2 and L2L1...Ch. 8.1 - Problems For problems 14-15, find L1L2 and L2L1...Ch. 8.1 - Problems If L1=D+a1(x), determine all differential...Ch. 8.1 - Problems For Problems 17-18, write the given...Ch. 8.1 - Prob. 18P Ch. 8.1 - Prob. 19P Ch. 8.1 - Prob. 20P Ch. 8.1 - Determine which of the following sets of vectors...Ch. 8.1 - Determine which of the following sets of vectors...Ch. 8.1 - For Problems 23-26, determine two linearly...Ch. 8.1 - For Problems 23-26, determine two linearly...Ch. 8.1 - For Problems 23-26, determine two linearly...Ch. 8.1 - For Problems 23-26, determine two linearly...Ch. 8.1 - For Problems 27-31, determine three linearly...Ch. 8.1 - For Problems 27-31, determine three linearly...Ch. 8.1 - For Problems 27-31, determine three linearly...Ch. 8.1 - Prob. 30P Ch. 8.1 - For Problems 27-31, determine three linearly...Ch. 8.1 - Prob. 32P Ch. 8.1 - For Problems 32-33, determine four linearly...Ch. 8.1 - For Problems 34-35, determine two linearly...Ch. 8.1 - For Problems 34-35, determine two linearly...Ch. 8.1 - For Problems 34-35, determine three linearly...Ch. 8.1 - Prob. 37P Ch. 8.1 - Determine a particular solution for the...Ch. 8.1 - Determine a particular solution for the...Ch. 8.1 - Prob. 40P Ch. 8.1 - Determine a particular solution for the...Ch. 8.1 - Prob. 42P Ch. 8.1 - Prob. 43P Ch. 8.1 - Extend the proof of theorem 8.1.4 to an arbitrary...Ch. 8.1 - Prob. 45P Ch. 8.1 - Let T:VW be a linear transformation, and suppose...Ch. 8.2 - True-False Review For Questions a-h, decide if the...Ch. 8.2 - True-False Review For Questions a-h, decide if the...Ch. 8.2 - Prob. 3TFR Ch. 8.2 - Prob. 4TFR Ch. 8.2 - True-False Review For Questions a-h, decide if the...Ch. 8.2 - Prob. 6TFR Ch. 8.2 - Prob. 7TFR Ch. 8.2 - Prob. 8TFR Ch. 8.2 - Problems For Problems 1-3, determine a basis for...Ch. 8.2 - Prob. 2P Ch. 8.2 - Problems For Problems 1-3, determine a basis for...Ch. 8.2 - Prob. 4P Ch. 8.2 - Prob. 5P Ch. 8.2 - Determine a basis for the solution space to y+4y=0...Ch. 8.2 - Determine a basis for the solution space to y+y=0...Ch. 8.2 - Problems For Problems 8-34, determine the general...Ch. 8.2 - Problems For Problems 8-34, determine the general...Ch. 8.2 - Problems For Problems 8-34, determine the general...Ch. 8.2 - Problems For Problems 8-34, determine the general...Ch. 8.2 - Problems For Problems 8-34, determine the general...Ch. 8.2 - Problems For Problems 8-34, determine the general...Ch. 8.2 - Problems For Problems 8-34, determine the general...Ch. 8.2 - Problems For Problems 8-34, determine the general...Ch. 8.2 - Problems For Problems 8-34, determine the general...Ch. 8.2 - Problems For Problems 8-34, determine the general...Ch. 8.2 - Problems For Problems 8-34, determine the general...Ch. 8.2 - Problems For Problems 8-34, determine the general...Ch. 8.2 - Problems For Problems 8-34, determine the general...Ch. 8.2 - Problems For Problems 8-34, determine the general...Ch. 8.2 - Problems For Problems 8-34, determine the general...Ch. 8.2 - Problems For Problems 8-34, determine the general...Ch. 8.2 - Problems For Problems 8-34, determine the general...Ch. 8.2 - Problems For Problems 8-34, determine the general...Ch. 8.2 - Problems For Problems 8-34, determine the general...Ch. 8.2 - Problems For Problems 8-34, determine the general...Ch. 8.2 - Problems For Problems 8-34, determine the general...Ch. 8.2 - Problems For Problems 8-34, determine the general...Ch. 8.2 - Problems For Problems 8-34, determine the general...Ch. 8.2 - Problems For Problems 8-34, determine the general...Ch. 8.2 - Problems For Problems 8-34, determine the general...Ch. 8.2 - Problems For Problems 8-34, determine the general...Ch. 8.2 - Problems For Problems 8-34, determine the general...Ch. 8.2 - Problems For Problems 35-38, solve the given...Ch. 8.2 - Problems For Problems 35-38, solve the given...Ch. 8.2 - Problems For Problems 35-38, solve the given...Ch. 8.2 - Problems For Problems 35-38, solve the given...Ch. 8.2 - Prob. 39P Ch. 8.2 - Prob. 40P Ch. 8.2 - Prob. 41P Ch. 8.2 - Prob. 42P Ch. 8.2 - Prob. 43P Ch. 8.2 - Problems Consider P(D)=y. What conditions on the...Ch. 8.2 - Prob. 45P Ch. 8.2 - Prob. 46P Ch. 8.2 - Prob. 47P Ch. 8.2 - Prob. 48P Ch. 8.2 - Prob. 49P Ch. 8.2 - Prob. 50P Ch. 8.2 - Prob. 51P Ch. 8.2 - Prob. 54P Ch. 8.3 - For Problem 1-16, determine the annihilator of the...Ch. 8.3 - For Problem 1-16, determine the annihilator of the...Ch. 8.3 - For Problem 1-16, determine the annihilator of the...Ch. 8.3 - For Problem 1-16, determine the annihilator of the...Ch. 8.3 - For Problem 1-16, determine the annihilator of the...Ch. 8.3 - For Problem 1-16, determine the annihilator of the...Ch. 8.3 - For Problem 1-16, determine the annihilator of the...Ch. 8.3 - For Problem 1-16, determine the annihilator of the...Ch. 8.3 - For Problem 1-16, determine the annihilator of the...Ch. 8.3 - For Problem 1-16, determine the annihilator of the...Ch. 8.3 - For Problem 1-16, determine the annihilator of the...Ch. 8.3 - For Problem 1-16, determine the annihilator of the...Ch. 8.3 - For Problem 1-16, determine the annihilator of the...Ch. 8.3 - For Problem 1-16, determine the annihilator of the...Ch. 8.3 - For Problem 1-16, determine the annihilator of the...Ch. 8.3 - For Problem 1-16, determine the annihilator of the...Ch. 8.3 - For Problems, 17-32, determine the general...Ch. 8.3 - For Problems, 17-32, determine the general...Ch. 8.3 - For Problems, 17-32, determine the general...Ch. 8.3 - For Problems, 17-32, determine the general...Ch. 8.3 - For Problems, 17-32, determine the general...Ch. 8.3 - For Problems, 17-32, determine the general...Ch. 8.3 - For Problems 17-32, determine the general solution...Ch. 8.3 - For Problems 17-32, determine the general solution...Ch. 8.3 - For Problems 17-32, determine the general solution...Ch. 8.3 - For Problems 17-32, determine the general solution...Ch. 8.3 - For Problems 17-32, determine the general solution...Ch. 8.3 - For Problems 17-32, determine the general solution...Ch. 8.3 - For Problems 17-32, determine the general solution...Ch. 8.3 - For Problems 17-32, determine the general solution...Ch. 8.3 - For Problems 17-32, determine the general solution...Ch. 8.3 - For Problems 17-32, determine the general solution...Ch. 8.3 - For Problem 33-37, solve the given initial value...Ch. 8.3 - For Problem 33-37, solve the given initial value...Ch. 8.3 - For Problems 33-37, solve the given initial value...Ch. 8.3 - For Problems 33-37, solve the given initial value...Ch. 8.3 - For Problems 33-37, solve the given initial value...Ch. 8.3 - At time t the displacement from equilibrium, y(t),...Ch. 8.3 - For Problems 39-47, determine an appropriate trial...Ch. 8.3 - For Problems 39-47, determine an appropriate trial...Ch. 8.3 - For Problems 39-47, determine an appropriate trial...Ch. 8.3 - For Problems 39-47, determine an appropriate trial...Ch. 8.3 - For Problems 39-47, determine an appropriate trial...Ch. 8.3 - Problems For problems 39-47, determine an...Ch. 8.3 - Prob. 45P Ch. 8.3 - Problems For problems 39-47, determine an...Ch. 8.3 - Problems For problems 39-47, determine an...Ch. 8.3 - Problems Derive an appropriate trial solution for...Ch. 8.5 - For Questions ai, decide if the given statement is...Ch. 8.5 - For Questions ai, decide if the given statement is...Ch. 8.5 - For Questions ai, decide if the given statement is...Ch. 8.5 - Prob. 4TFR Ch. 8.5 - For Questions ai, decide if the given statement is...Ch. 8.5 - Prob. 6TFR Ch. 8.5 - Prob. 7TFR Ch. 8.5 - Prob. 8TFR Ch. 8.5 - Prob. 9TFR Ch. 8.5 - Prob. 1P Ch. 8.5 - Prob. 2P Ch. 8.5 - A force of 3N stretches a spring by 1m. a Find the...Ch. 8.5 - For Problems 4-10, determine the motion of the...Ch. 8.5 - For Problems 4-10, determine the motion of the...Ch. 8.5 - For Problems 4-10, determine the motion of the...Ch. 8.5 - For Problems 4-10, determine the motion of the...Ch. 8.5 - For Problems 4-10, determine the motion of the...Ch. 8.5 - For Problems 4-10, determine the motion of the...Ch. 8.5 - Prob. 10P Ch. 8.5 - In the previous problem, find the time at which...Ch. 8.5 - Consider the spring-mass system whose motion is...Ch. 8.5 - Consider the spring-mass system whose motion is...Ch. 8.5 - Consider the spring-mass system whose motion is...Ch. 8.5 - Prob. 15P Ch. 8.5 - Prob. 16P Ch. 8.5 - Prob. 18P Ch. 8.5 - Prob. 19P Ch. 8.5 - Prob. 20P Ch. 8.5 - Prob. 21P Ch. 8.5 - An object of mass m is attached to the midpoint of...Ch. 8.5 - Repeat the previous problem if the string has...Ch. 8.5 - Consider the damped spring-mass system whose...Ch. 8.5 - Consider the spring-mass system whose motion is...Ch. 8.5 - Consider the spring-mass system whose motion is...Ch. 8.5 - Prob. 27P Ch. 8.5 - The general solution of forced undamped...Ch. 8.5 - Determine the period of the motion for the...Ch. 8.5 - Prob. 30P Ch. 8.5 - Prob. 31P Ch. 8.5 - Consider the damped spring-mass system with m=1,...Ch. 8.5 - Consider the spring-mass system whose motion is...Ch. 8.5 - Prob. 34P Ch. 8.6 - For Questions af, decide if the given statement is...Ch. 8.6 - Prob. 2TFR Ch. 8.6 - Prob. 3TFR Ch. 8.6 - For Questions af, decide if the given statement is...Ch. 8.6 - Prob. 5TFR Ch. 8.6 - Prob. 6TFR Ch. 8.6 - Problems Determine the charge on the capacitor at...Ch. 8.6 - Problems Determine the steady current in the RLC...Ch. 8.6 - Prob. 3P Ch. 8.6 - Prob. 4P Ch. 8.6 - Consider the RLC circuit with R=16, L=8H, C=140F,...Ch. 8.6 - Show that the differential equation governing the...Ch. 8.6 - Prob. 7P Ch. 8.6 - Prob. 8P Ch. 8.7 - Problems For Problems 122, use the variation of...Ch. 8.7 - Problems For Problems 122, use the variation of...Ch. 8.7 - Problems For Problems 122, use the variation of...Ch. 8.7 - Problems For Problems 122, use the variation of...Ch. 8.7 - Problems For Problems 122, use the variation of...Ch. 8.7 - Problems For Problems 122, use the variation of...Ch. 8.7 - Problems For Problems 122, use the variation of...Ch. 8.7 - Problems For Problems 122, use the variation of...Ch. 8.7 - Problems For Problems 122, use the...Ch. 8.7 - Problems For Problems 122, use the...Ch. 8.7 - Problems For Problems 122, use the...Ch. 8.7 - Prob. 12P Ch. 8.7 - Prob. 13P Ch. 8.7 - Problems For Problems 122, use the...Ch. 8.7 - Problems For Problems 1-22, use the...Ch. 8.7 - Problems For Problems 1-22, use the...Ch. 8.7 - Prob. 17P Ch. 8.7 - Prob. 18P Ch. 8.7 - Prob. 19P Ch. 8.7 - Prob. 20P Ch. 8.7 - Prob. 21P Ch. 8.7 - Prob. 22P Ch. 8.7 - Problems For Problems 23-26, use a Greens...Ch. 8.7 - Problems For Problems 23-26, use a Greens...Ch. 8.7 - Problems For problems 23-26, use a Greens function...Ch. 8.7 - Problems For problems 23-26, use a Greens function...Ch. 8.7 - Problems For problem 27-28, use a Greens function...Ch. 8.7 - Prob. 28P Ch. 8.7 - Prob. 29P Ch. 8.7 - Problems Consider the differential equation...Ch. 8.7 - Prob. 31P Ch. 8.7 - Prob. 32P Ch. 8.7 - Prob. 33P Ch. 8.7 - Prob. 34P Ch. 8.7 - Prob. 35P Ch. 8.7 - Prob. 36P Ch. 8.7 - Prob. 37P Ch. 8.8 - Problems For Problems 1-8, determine the general...Ch. 8.8 - Problems For Problems 1-8, determine the general...Ch. 8.8 - Problems For Problems 1-8, determine the general...Ch. 8.8 - Problems For Problems 1-8, determine the general...Ch. 8.8 - Problems For Problems 1-8, determine the general...Ch. 8.8 - Problems For Problems 1-8, determine the general...Ch. 8.8 - Problems For Problems 1-8, determine the general...Ch. 8.8 - Problems For Problems 1-8, determine the general...Ch. 8.8 - Problems For Problems 9-11, find the solution to...Ch. 8.8 - Prob. 10P Ch. 8.8 - Prob. 11P Ch. 8.8 - Problems Consider the Cauchy-Euler equation ...Ch. 8.8 - Problems For Problems 14-21, solve the given...Ch. 8.8 - Problems For Problems 14-21, solve the given...Ch. 8.8 - Problems For Problems 14-21, solve the given...Ch. 8.8 - Problems For Problems 14-21, solve the given...Ch. 8.8 - Prob. 18P Ch. 8.8 - Problems For Problems 14-21, solve the given...Ch. 8.8 - Prob. 20P Ch. 8.8 - Prob. 21P Ch. 8.8 - Prob. 24P Ch. 8.9 - For Problems 16, y1 is a solution to the given...Ch. 8.9 - For Problems 16, y1 is a solution to the given...Ch. 8.9 - For Problems 16, y1 is a solution to the given...Ch. 8.9 - For Problems 16, y1 is a solution to the given...Ch. 8.9 - For Problems 16, y1 is a solution to the given...Ch. 8.9 - For Problems 16, y1 is a solution to the given...Ch. 8.9 - Consider the Cauchy-Euler equation...Ch. 8.9 - Prob. 8P Ch. 8.9 - Prob. 9P Ch. 8.9 - For Problems 1015, y1 is a solution to the...Ch. 8.9 - For Problems 1015, y1 is a solution to the...Ch. 8.9 - Prob. 12P Ch. 8.9 - Prob. 13P Ch. 8.9 - Prob. 14P Ch. 8.9 - For Problems 1015, y1 is a solution to the...Ch. 8.9 - Consider the differential equation...Ch. 8.10 - In Problems 1-6, find Ly for the given...Ch. 8.10 - Prob. 2AP Ch. 8.10 - Prob. 3AP Ch. 8.10 - Prob. 4AP Ch. 8.10 - Prob. 5AP Ch. 8.10 - Prob. 6AP Ch. 8.10 - Prob. 7AP Ch. 8.10 - Prob. 8AP Ch. 8.10 - Prob. 9AP Ch. 8.10 - Prob. 10AP Ch. 8.10 - Prob. 11AP Ch. 8.10 - Prob. 12AP Ch. 8.10 - Prob. 13AP Ch. 8.10 - In Problem 14-17, determine the annihilator of the...Ch. 8.10 - Prob. 15AP Ch. 8.10 - Prob. 16AP Ch. 8.10 - Prob. 17AP Ch. 8.10 - Prob. 18AP Ch. 8.10 - In Problem 18-23, determine a trial solution for...Ch. 8.10 - Prob. 20AP Ch. 8.10 - Prob. 21AP Ch. 8.10 - Prob. 22AP Ch. 8.10 - Prob. 23AP Ch. 8.10 - For Problems 24-29, solve the given nonhomogeneous...Ch. 8.10 - Prob. 25AP Ch. 8.10 - For Problems 24-29, solve the given nonhomogeneous...Ch. 8.10 - Prob. 27AP Ch. 8.10 - Prob. 28AP Ch. 8.10 - Prob. 29AP Ch. 8.10 - Prob. 30AP Ch. 8.10 - Prob. 31AP Ch. 8.10 - Prob. 32AP Ch. 8.10 - For Problem 30-39, state whether the annihilator...Ch. 8.10 - Prob. 34AP Ch. 8.10 - For Problem 30-39, state whether the annihilator...Ch. 8.10 - For Problem 30-39, state whether the annihilator...Ch. 8.10 - Prob. 37AP Ch. 8.10 - Prob. 38AP Ch. 8.10 - For Problem 30-39, state whether the annihilator...Ch. 8.10 - Prob. 40AP Ch. 8.10 - For Problems 40-45, use the annihilator to solve...Ch. 8.10 - Prob. 42AP Ch. 8.10 - Prob. 43AP Ch. 8.10 - Prob. 44AP Ch. 8.10 - Prob. 45AP Ch. 8.10 - Prob. 46AP Ch. 8.10 - Prob. 47AP Ch. 8.10 - For Problem 47-51, use the variations of...Ch. 8.10 - Prob. 49AP Ch. 8.10 - Prob. 50AP Ch. 8.10 - Prob. 51AP Ch. 8.10 - Prob. 52AP Ch. 8.10 - Prob. 53AP Ch. 8.10 - In the Problem 53-58, find the general solution to...Ch. 8.10 - Prob. 55AP Ch. 8.10 - In the Problem 53-58, find the general solution to...Ch. 8.10 - Prob. 57AP Ch. 8.10 - Prob. 58AP Ch. 8.10 - For Problems 59-61, solve the differential...Ch. 8.10 - Prob. 60AP Ch. 8.10 - Prob. 61AP Ch. 8.10 - Prob. 62AP Ch. 8.10 - Prob. 63AP Ch. 8.10 - Prob. 64AP Ch. 8.10 - Prob. 65AP Ch. 8.10 - Prob. 66AP

Knowledge Booster

Background pattern image

$Algebra$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

Similar questions

SEE MORE QUESTIONS

Recommended textbooks for you

Algebra and Trigonometry (6th Edition)
Algebra
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:9781305657960
Author:Joseph Gallian
Publisher:Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:9781285463247
Author:David Poole
Publisher:Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:9780135163078
Author:Michael Sullivan
Publisher:PEARSON
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:9780980232776
Author:Gilbert Strang
Publisher:Wellesley-Cambridge Press
College Algebra (Collegiate Math)
Algebra
ISBN:9780077836344
Author:Julie Miller, Donna Gerken
Publisher:McGraw-Hill Education

Text book image

Algebra and Trigonometry (6th Edition)

Algebra

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:PEARSON

Text book image

Contemporary Abstract Algebra

Algebra

ISBN:9781305657960

Author:Joseph Gallian

Publisher:Cengage Learning

Text book image

Linear Algebra: A Modern Introduction

Algebra

ISBN:9781285463247

Author:David Poole

Publisher:Cengage Learning

Text book image

Algebra And Trigonometry (11th Edition)

Algebra

ISBN:9780135163078

Author:Michael Sullivan

Publisher:PEARSON

Text book image

Introduction to Linear Algebra, Fifth Edition

Algebra

ISBN:9780980232776

Author:Gilbert Strang

Publisher:Wellesley-Cambridge Press

Text book image

College Algebra (Collegiate Math)

Algebra

ISBN:9780077836344

Author:Julie Miller, Donna Gerken

Publisher:McGraw-Hill Education

SEE MORE TEXTBOOKS

01 - What Is A Differential Equation in Calculus? Learn to Solve Ordinary Differential Equations.; Author: Math and Science;https://www.youtube.com/watch?v=K80YEHQpx9g;License: Standard YouTube License, CC-BY

Higher Order Differential Equation with constant coefficient (GATE) (Part 1) l GATE 2018; Author: GATE Lectures by Dishank;https://www.youtube.com/watch?v=ODxP7BbqAjA;License: Standard YouTube License, CC-BY

Solution of Differential Equations and Initial Value Problems; Author: Jefril Amboy;https://www.youtube.com/watch?v=Q68sk7XS-dc;License: Standard YouTube License, CC-BY