Skip to main content

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

Problems Problems 26-32, solve the given initial-value problem up to the evaluation of a convolution integral. y ′ ′ + 16 y = f ( t ) , y ( 0 ) = α , y ′ ( 0 ) = β , where α and β are constants.

Problems Problems 26-32, solve the given initial-value problem up to the evaluation of a convolution integral. y ′ ′ + 16 y = f ( t ) , y ( 0 ) = α , y ′ ( 0 ) = β , where α and β are constants.

Solution Summary: The author explains the initial value problem y(t) by Laplace transforms.

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

Videos

Textbook Question

Chapter 10.9, Problem 28P

Problems

Problems 26-32, solve the given initial-value problem up to the evaluation of a convolution integral.

y ′ ′ + 16 y = f ( t ) , y ( 0 ) = α , y ′ ( 0 ) = β , where α and β are constants.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

Blurred answer

Chapter 10.9, Problem 27P

Chapter 10.9, Problem 29P

Chapter 10 Solutions

Differential Equations and Linear Algebra (4th Edition)

Ch. 10.1 - For Questions a-i, decide if the given statement...Ch. 10.1 - For Questions a-i, decide if the given statement...Ch. 10.1 - For Questions a-i, decide if the given statement...Ch. 10.1 - For Questions a-i, decide if the given statement...Ch. 10.1 - For Questions a-i, decide if the given statement...Ch. 10.1 - For Questions a-i, decide if the given statement...Ch. 10.1 - Prob. 7TFR Ch. 10.1 - For Questions a-i, decide if the given statement...Ch. 10.1 - For Questions a-i, decide if the given statement...Ch. 10.1 - Problems For Problems 1-12, use 10.1.1 to...

Ch. 10.1 - Problems For Problems 1-12, use 10.1.1 to...Ch. 10.1 - Problems For Problems 1-12, use 10.1.1 to...Ch. 10.1 - Problems For Problems 1-12, use 10.1.1 to...Ch. 10.1 - Problems For Problems 1-12, use 10.1.1 to...Ch. 10.1 - Prob. 6P Ch. 10.1 - Problems For Problems 1-12, use 10.1.1 to...Ch. 10.1 - Prob. 8P Ch. 10.1 - Problems For Problems 1-12, use 10.1.1 to...Ch. 10.1 - Prob. 10P Ch. 10.1 - Problems For Problems 1-12, use 10.1.1 to...Ch. 10.1 - Prob. 12P Ch. 10.1 - Problems For Problems 13-22, use the linearity of...Ch. 10.1 - Prob. 14P Ch. 10.1 - Problems For Problems 13-22, use the linearity of...Ch. 10.1 - PROBLEMNS For Problems 13-22, use the linearity of...Ch. 10.1 - Prob. 17P Ch. 10.1 - PROBLEMNS For Problems 13-22, use the linearity of...Ch. 10.1 - PROBLEMNS For Problems 13-22, use the linearity of...Ch. 10.1 - PROBLEMNS For Problems 13-22, use the linearity of...Ch. 10.1 - PROBLEMNS For Problems 13-22, use the linearity of...Ch. 10.1 - PROBLEMNS For Problems 13-22, use the linearity of...Ch. 10.1 - PROBLEMNS For Problems 23-30, sketch the given...Ch. 10.1 - Prob. 24P Ch. 10.1 - PROBLEMNS For Problems 23-30, sketch the given...Ch. 10.1 - Prob. 26P Ch. 10.1 - For Problems 23-30, sketch the given function and...Ch. 10.1 - For Problems 23-30, sketch the given function and...Ch. 10.1 - For Problems 23-30, sketch the given function and...Ch. 10.1 - For Problems 23-30, sketch the given function and...Ch. 10.1 - For Problems 31-34, sketch the given function and...Ch. 10.1 - For Problems 31-34, sketch the given function and...Ch. 10.1 - For Problems 31-34, sketch the given function and...Ch. 10.1 - Prob. 34P Ch. 10.1 - Prob. 35P Ch. 10.1 - Prob. 36P Ch. 10.1 - Use mathematical induction to prove that for every...Ch. 10.1 - Prob. 38P Ch. 10.2 - True-False Review For Questions (a)-(f) decide if...Ch. 10.2 - True-False Review For Questions (a)-(f) decide if...Ch. 10.2 - Prob. 3TFR Ch. 10.2 - Prob. 4TFR Ch. 10.2 - Prob. 5TFR Ch. 10.2 - Prob. 6TFR Ch. 10.2 - Prob. 1P Ch. 10.2 - Prob. 2P Ch. 10.2 - Prob. 3P Ch. 10.2 - Prob. 4P Ch. 10.2 - For Problem 1-5, show that the given function is...Ch. 10.2 - Prob. 6P Ch. 10.2 - Prob. 7P Ch. 10.2 - For Problem 7-21, determine the inverse Laplace...Ch. 10.2 - For Problem 7-21, determine the inverse Laplace...Ch. 10.2 - For Problem 7-21, determine the inverse Laplace...Ch. 10.2 - For Problem 7-21, determine the inverse Laplace...Ch. 10.2 - For Problem 7-21, determine the inverse Laplace...Ch. 10.2 - For Problem 7-21, determine the inverse Laplace...Ch. 10.2 - Prob. 14P Ch. 10.2 - For Problem 7-21, determine the inverse Laplace...Ch. 10.2 - Prob. 16P Ch. 10.2 - For Problem 7-21, determine the inverse Laplace...Ch. 10.2 - For Problem 7-21, determine the inverse Laplace...Ch. 10.2 - For Problem 7-21, determine the inverse Laplace...Ch. 10.2 - For Problem 7-21, determine the inverse Laplace...Ch. 10.2 - Problems For Problem 7-21, determine the inverse...Ch. 10.2 - Prob. 22P Ch. 10.3 - For Questions (a)-(h) decide if the given...Ch. 10.3 - Prob. 2TFR Ch. 10.3 - Prob. 3TFR Ch. 10.3 - Prob. 4TFR Ch. 10.3 - Prob. 5TFR Ch. 10.3 - Prob. 6TFR Ch. 10.3 - True-False Review For Questions (a)-(h) decide if...Ch. 10.3 - Problems For Problems 1-9, determine the Laplace...Ch. 10.3 - Prob. 2P Ch. 10.3 - Problems For Problem 1-9, determine the Laplace...Ch. 10.3 - Prob. 4P Ch. 10.3 - Problems For Problem 1-9, determine the Laplace...Ch. 10.3 - Prob. 6P Ch. 10.3 - Problems For Problem 1-9, determine the Laplace...Ch. 10.3 - Prob. 8P Ch. 10.3 - Problems For Problem 1-9, determine the Laplace...Ch. 10.3 - Prob. 10P Ch. 10.3 - Prob. 11P Ch. 10.4 - For Questions a-d, decide if the given statement...Ch. 10.4 - Prob. 2TFR Ch. 10.4 - Prob. 3TFR Ch. 10.4 - Prob. 4TFR Ch. 10.4 - Problems For problem 1-27, use the Laplace...Ch. 10.4 - Problems For problems 1-27, use the Laplace...Ch. 10.4 - Problems For problem 1-27, use the Laplace...Ch. 10.4 - Problems For problem 1-27, use the Laplace...Ch. 10.4 - Problems For problem 1-27, use the Laplace...Ch. 10.4 - Prob. 6P Ch. 10.4 - Problems For problem 1-27, use the Laplace...Ch. 10.4 - Problems For problem 1-27, use the Laplace...Ch. 10.4 - Problems For problem 1-27, use the Laplace...Ch. 10.4 - Problems For problem 1-27, use the Laplace...Ch. 10.4 - Problems For problem 1-27, use the Laplace...Ch. 10.4 - Problems For problem 1-27, use the Laplace...Ch. 10.4 - Problems For problems 1-27, use the Laplace...Ch. 10.4 - Prob. 14P Ch. 10.4 - Problems For problem 1-27, use the Laplace...Ch. 10.4 - Problems For problem 1-27, use the Laplace...Ch. 10.4 - Problems For problem 1-27, use the Laplace...Ch. 10.4 - Problems For problem 1-27, use the Laplace...Ch. 10.4 - Prob. 19P Ch. 10.4 - Problems For problem 1-27, use the Laplace...Ch. 10.4 - Prob. 21P Ch. 10.4 - Prob. 22P Ch. 10.4 - Prob. 23P Ch. 10.4 - Prob. 24P Ch. 10.4 - Problems For problem 1-27, use the Laplace...Ch. 10.4 - Prob. 26P Ch. 10.4 - Problems For problem 1-27, use the Laplace...Ch. 10.4 - Prob. 28P Ch. 10.4 - Prob. 29P Ch. 10.4 - Prob. 30P Ch. 10.4 - Prob. 31P Ch. 10.4 - Prob. 32P Ch. 10.4 - Prob. 34P Ch. 10.5 - True-False Review For Questions (a)(h), decide if...Ch. 10.5 - Prob. 2TFR Ch. 10.5 - True-False Review For Questions (a)(h), decide if...Ch. 10.5 - Prob. 4TFR Ch. 10.5 - Prob. 5TFR Ch. 10.5 - Prob. 6TFR Ch. 10.5 - Prob. 7TFR Ch. 10.5 - Prob. 8TFR Ch. 10.5 - For Problems 1-11, determine f(ta) for the given...Ch. 10.5 - Prob. 2P Ch. 10.5 - Prob. 3P Ch. 10.5 - Prob. 4P Ch. 10.5 - For Problems 1-11, determine f(ta) for the given...Ch. 10.5 - Prob. 6P Ch. 10.5 - Prob. 7P Ch. 10.5 - Prob. 8P Ch. 10.5 - Prob. 9P Ch. 10.5 - Prob. 10P Ch. 10.5 - Prob. 11P Ch. 10.5 - Prob. 12P Ch. 10.5 - For Problems 12-17, determine f(t). f(t1)=(t2)2.Ch. 10.5 - Prob. 14P Ch. 10.5 - For Problems 12-17, determine f(t)....Ch. 10.5 - Prob. 16P Ch. 10.5 - Prob. 17P Ch. 10.5 - For Problems 18-27, determine the Laplace...Ch. 10.5 - For Problems 18-27, determine the Laplace...Ch. 10.5 - For Problems 18-27, determine the Laplace...Ch. 10.5 - For Problems 18-27, determine the Laplace...Ch. 10.5 - For Problems 18-27, determine the Laplace...Ch. 10.5 - Prob. 23P Ch. 10.5 - For Problems 18-27, determine the Laplace...Ch. 10.5 - For Problems 18-27, determine the Laplace...Ch. 10.5 - Prob. 26P Ch. 10.5 - For Problems 18-27, determine the Laplace...Ch. 10.5 - Prob. 28P Ch. 10.5 - For Problems 28-42, determine L1[F]. F(s)=4(s+2)3.Ch. 10.5 - Prob. 30P Ch. 10.5 - For Problems 28-42, determine L1[F]....Ch. 10.5 - Prob. 32P Ch. 10.5 - For Problems 28-42, determine L1[F]....Ch. 10.5 - Prob. 34P Ch. 10.5 - Prob. 35P Ch. 10.5 - Prob. 36P Ch. 10.5 - For Problems 28-42, determine L1[F]....Ch. 10.5 - Prob. 38P Ch. 10.5 - For Problems 28-42, determine L1[F]....Ch. 10.5 - Prob. 40P Ch. 10.5 - For Problems 28-42, determine L1[F]....Ch. 10.5 - Prob. 42P Ch. 10.5 - For Problems 43-53, solve the given initial-value...Ch. 10.5 - Prob. 44P Ch. 10.5 - For Problems 43-53, solve the given initial-value...Ch. 10.5 - Prob. 46P Ch. 10.5 - For Problems 43-53, solve the given initial-value...Ch. 10.5 - For Problems 43-53, solve the given initial-value...Ch. 10.5 - For Problems 43-53, solve the given initial-value...Ch. 10.5 - Prob. 50P Ch. 10.5 - Prob. 51P Ch. 10.5 - For Problems 43-53, solve the given initial-value...Ch. 10.5 - For Problems 43-53, solve the given initial-value...Ch. 10.5 - Prob. 54P Ch. 10.5 - Prob. 55P Ch. 10.6 - For Questions a-d, decide if the given statement...Ch. 10.6 - For Questions a-d, decide if the given statement...Ch. 10.6 - Prob. 3TFR Ch. 10.6 - Prob. 4TFR Ch. 10.6 - Problems: For Problems 1-7, make a sketch of the...Ch. 10.6 - Problems: For Problems 1-7, make a sketch of the...Ch. 10.6 - Problems: For Problems 1-7, make a sketch of the...Ch. 10.6 - Problems: For Problems 1-7, make a sketch of the...Ch. 10.6 - Problems: For Problems 1-7, make a sketch of the...Ch. 10.6 - Prob. 6P Ch. 10.6 - Prob. 7P Ch. 10.6 - Problems: For Problems 8-15, make a sketch of the...Ch. 10.6 - Problems: For Problems 8-15, make a sketch of the...Ch. 10.6 - Problems: For Problems 8-15, make a sketch of the...Ch. 10.6 - Problems: For Problems 8-15, make a sketch of the...Ch. 10.6 - Problems: For Problems 8-15, make a sketch of the...Ch. 10.6 - Problems: For Problems 8-15, make a sketch of the...Ch. 10.6 - Problems: For Problems 8-15, make a sketch of the...Ch. 10.6 - Prob. 15P Ch. 10.7 - True-False Review For Questions (a)(g), decide if...Ch. 10.7 - Prob. 2TFR Ch. 10.7 - Prob. 3TFR Ch. 10.7 - Prob. 4TFR Ch. 10.7 - Prob. 5TFR Ch. 10.7 - Prob. 7TFR Ch. 10.7 - Problems For Problems 1-11, determine the...Ch. 10.7 - Problems For Problems 1-11, determine the...Ch. 10.7 - Problems For Problems 1-11, determine the...Ch. 10.7 - Problems For Problems 1-11, determine the...Ch. 10.7 - Problems For Problems 1-11, determine the...Ch. 10.7 - Problems For Problems 1-11, determine the...Ch. 10.7 - Problems For Problems 1-11, determine the...Ch. 10.7 - Problems For Problems 1-11, determine the...Ch. 10.7 - Problems For Problems 1-11, determine the...Ch. 10.7 - Prob. 10P Ch. 10.7 - Problems For Problems 1-11, determine the...Ch. 10.7 - Problems For Problems 12-26, determine the...Ch. 10.7 - Problems For Problems 12-26, determine the...Ch. 10.7 - Prob. 14P Ch. 10.7 - Problems For Problems 12-26, determine the...Ch. 10.7 - Prob. 16P Ch. 10.7 - Problems For Problems 12-26, determine the...Ch. 10.7 - Prob. 18P Ch. 10.7 - Problems For Problems 12-26, determine the...Ch. 10.7 - Prob. 20P Ch. 10.7 - Problems For Problems 12-26, determine the...Ch. 10.7 - Prob. 22P Ch. 10.7 - Prob. 23P Ch. 10.7 - Prob. 24P Ch. 10.7 - Problems For Problems 12-26, determine the...Ch. 10.7 - Prob. 26P Ch. 10.7 - For Problems 27-41, solve the given initial-value...Ch. 10.7 - Prob. 28P Ch. 10.7 - Prob. 29P Ch. 10.7 - Prob. 30P Ch. 10.7 - Prob. 31P Ch. 10.7 - Problems For Problems 27-41, solve the given...Ch. 10.7 - For Problems 27-41, solve the given initial-value...Ch. 10.7 - For Problems 27-41, solve the given initial-value...Ch. 10.7 - For Problems 27-41, solve the given initial-value...Ch. 10.7 - Prob. 36P Ch. 10.7 - Prob. 37P Ch. 10.7 - Problems For Problems 27-41, solve the given...Ch. 10.7 - Prob. 39P Ch. 10.7 - Problems For Problems 27-41, solve the given...Ch. 10.7 - Prob. 41P Ch. 10.7 - Problems For Problems 42-45, solve the given...Ch. 10.7 - For Problems 4245, solve the given initial value...Ch. 10.7 - Prob. 48P Ch. 10.8 - For Questions a-d, decide if the given statement...Ch. 10.8 - For Questions a-d, decide if the given statement...Ch. 10.8 - Prob. 3TFR Ch. 10.8 - Prob. 4TFR Ch. 10.8 - Prob. 5TFR Ch. 10.8 - For Problem 1-13, solve the given initial value...Ch. 10.8 - For Problem 1-13, solve the given initial value...Ch. 10.8 - For Problem 1-13, solve the given initial value...Ch. 10.8 - Prob. 4P Ch. 10.8 - For Problem 1-13, solve the given initial value...Ch. 10.8 - Prob. 6P Ch. 10.8 - For Problem 1-13, solve the given initial value...Ch. 10.8 - Prob. 8P Ch. 10.8 - For Problem 1-13, solve the given initial value...Ch. 10.8 - Prob. 10P Ch. 10.8 - Prob. 11P Ch. 10.8 - Prob. 12P Ch. 10.8 - For Problems 1-13, solve the given initial value...Ch. 10.8 - The motion of a spring-mass system is governed by...Ch. 10.8 - Prob. 15P Ch. 10.8 - Prob. 16P Ch. 10.9 - True-False Review For Questions (a)(g), decide if...Ch. 10.9 - Prob. 2TFR Ch. 10.9 - True-False Review For Questions (a)(g), decide if...Ch. 10.9 - True-False Review For Questions (a)(g), decide if...Ch. 10.9 - Prob. 6TFR Ch. 10.9 - Prob. 7TFR Ch. 10.9 - Problems For Problems 1-6, determine fg. f(t)=t,...Ch. 10.9 - Problems For Problems 1-6, determine fg. f(t)=6t2,...Ch. 10.9 - Prob. 3P Ch. 10.9 - Problems For Problems 1-6, determine fg. f(t)=et,...Ch. 10.9 - Problems For Problems 1-6, determine fg. f(t)=t2,...Ch. 10.9 - Problems For Problems 1-6, determine fg. f(t)=et,...Ch. 10.9 - Problems Prove that fg=gf.Ch. 10.9 - Problems Prove that f(gh)=(fg)h.Ch. 10.9 - Problems Prove that f(g+h)=(fg)+(fh).Ch. 10.9 - Problems For Problems 10-14, determine L(fg)....Ch. 10.9 - Problems For Problems 10-14, determine L(fg)....Ch. 10.9 - Problems For Problems 10-14, determine L(fg)....Ch. 10.9 - Problems For Problems 10-14, determine L(fg)....Ch. 10.9 - Prob. 14P Ch. 10.9 - Problems For Problems 15-20, determine...Ch. 10.9 - Problems For Problems 15-20, determine...Ch. 10.9 - Prob. 17P Ch. 10.9 - Prob. 18P Ch. 10.9 - Prob. 19P Ch. 10.9 - Prob. 21P Ch. 10.9 - Problems For Problems 21-25, express L1[F(s)G(s)]...Ch. 10.9 - Problems For Problems 21-25, express L1[F(s)G(s)]...Ch. 10.9 - Prob. 24P Ch. 10.9 - Problems For Problems 21-25, express L1[F(s)G(s)]...Ch. 10.9 - Prob. 26P Ch. 10.9 - Problems Problems 26-32, solve the given...Ch. 10.9 - Problems Problems 26-32, solve the given...Ch. 10.9 - Problems Problems 26-32, solve the given...Ch. 10.9 - Problems Problems 26-32, solve the given...Ch. 10.9 - Prob. 31P Ch. 10.9 - Prob. 32P Ch. 10.9 - Prob. 33P Ch. 10.9 - Prob. 34P Ch. 10.9 - Prob. 35P Ch. 10.9 - Prob. 36P Ch. 10.9 - Prob. 37P Ch. 10.9 - Prob. 38P Ch. 10.9 - Prob. 39P Ch. 10.10 - Prob. 1AP Ch. 10.10 - Prob. 2AP Ch. 10.10 - Prob. 3AP Ch. 10.10 - Prob. 4AP Ch. 10.10 - Prob. 5AP Ch. 10.10 - Prob. 7AP Ch. 10.10 - Prob. 8AP Ch. 10.10 - Prob. 9AP Ch. 10.10 - Prob. 10AP Ch. 10.10 - For Problems 11-19, use properties of the Laplace...Ch. 10.10 - Prob. 12AP Ch. 10.10 - Prob. 13AP Ch. 10.10 - Prob. 14AP Ch. 10.10 - For Problems 11-19, use properties of the Laplace...Ch. 10.10 - Prob. 16AP Ch. 10.10 - Prob. 17AP Ch. 10.10 - Prob. 18AP Ch. 10.10 - Prob. 19AP Ch. 10.10 - Prob. 20AP Ch. 10.10 - For Problems 20-25, determine a function f(t) that...Ch. 10.10 - For problems 20-25, determine a function f(t) that...Ch. 10.10 - For problems 20-25, determine a function f(t) that...Ch. 10.10 - For problems 20-25, determine a function f(t) that...Ch. 10.10 - For problems 20-25, determine a function f(t) that...Ch. 10.10 - Prob. 26AP Ch. 10.10 - For Problems 26-28, sketch f(t), express f(t) in...Ch. 10.10 - For Problems 26-28, sketch f(t), express f(t) in...Ch. 10.10 - Prob. 29AP Ch. 10.10 - Prob. 30AP Ch. 10.10 - Prob. 31AP Ch. 10.10 - Let y(t) be the solution to the initial-value...Ch. 10.10 - Show that the general solution to the...Ch. 10.10 - For Problems 34-40, use the Laplace transform to...Ch. 10.10 - For Problems 34-40, use the Laplace transform to...Ch. 10.10 - For Problems 34-40, use the Laplace transform to...Ch. 10.10 - For Problems 34-40, use the Laplace transform to...Ch. 10.10 - For Problems 34-40, use the Laplace transform to...Ch. 10.10 - Prob. 39AP Ch. 10.10 - For Problems 34-40, use the Laplace transform to...Ch. 10.10 - For Problems 41-44, use the Laplace transform to...Ch. 10.10 - For Problems 41-44, use the Laplace transform to...Ch. 10.10 - For Problems 41-44, use the Laplace transform to...Ch. 10.10 - For Problems 41-44, use the Laplace transform to...Ch. 10.10 - Prob. 45AP Ch. 10.10 - Prob. 46AP Ch. 10.10 - For Problems 45-48, use the Laplace transform to...Ch. 10.10 - Prob. 48AP

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.

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

Intro to the Laplace Transform & Three Examples; Author: Dr. Trefor Bazett;https://www.youtube.com/watch?v=KqokoYr_h1A;License: Standard YouTube License, CC-BY