Explanation Given data: y ″ + y = 0 Formula used: Write the expression for solution of second order linear homogeneous differential equation. y ( x ) = c 1 y 1 ( x ) + c 2 y 2 ( x ) (1) Here, c 1 and c 2 are constants, y 1 ( x ) and y 2 ( x ) are solution of linear homogeneous equation. Consider the second order linear homogeneous differential equation as follows. y ″ + y = 0 (2) Consider the general expression for second order linear homogeneous differential equation as follows. P ( x ) y ″ + Q ( x ) y ′ + R ( x ) y = 0 (3) Compare equations (2) and (3). P ( x ) = 1 Q ( x ) = 0 R ( x ) = 1 The linear homogeneous differential equation consists of two solutions y ″ and y represents as follows. y ″ = ( c 1 y 1 + c 2 y 2 ) ′ ′ y ′ = ( c 1 y 1 + c 2 y 2 ) ′ y = c 1 y 1 + c 2 y 2 Modify equation (2) as follows. y 1 ′ ′ + y 1 = 0 Modify equation (2) as follows. y 2 ′ ′ + y 2 = 0 Consider right hand side (R.H.S) of equation (3)

8th Edition

ISBN: 9781285741550

Author: James Stewart

Publisher: Cengage Learning

See similar textbooks

Concept explainers

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.

Videos

Question

Chapter 17, Problem 1RQ

To determine

Whether the statement “If y1 and y2 are solutions of y″+y=0 , then y1+y2 is also a solution of the equation” is true or false.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 17, Problem 5RCC

Chapter 17, Problem 2RQ

Chapter 17 Solutions

Calculus: Early Transcendentals

Knowledge Booster

$Calculus$

Learn more about

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

Similar questions

Find three solutions to this equation: y=2x+3 .
Find three solutions to the linear equation y=2x4 .
Complete the table to find three solutions to this equation: y=3x1 .

Recommended textbooks for you

Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
College Algebra
Algebra
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:Cengage Learning
Algebra: Structure And Method, Book 1
Algebra
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:McDougal Littell
Elementary Algebra
Algebra
ISBN:9780998625713
Author:Lynn Marecek, MaryAnne Anthony-Smith
Publisher:OpenStax - Rice University
Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:Cengage Learning

Glencoe Algebra 1, Student Edition, 9780079039897...

Algebra

ISBN:9780079039897

Author:Carter

Publisher:McGraw Hill

College Algebra

Algebra

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:Cengage Learning

Algebra: Structure And Method, Book 1

Algebra

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:McDougal Littell

Elementary Algebra

Algebra

ISBN:9780998625713

Author:Lynn Marecek, MaryAnne Anthony-Smith

Publisher:OpenStax - Rice University

Holt Mcdougal Larson Pre-algebra: Student Edition...

Algebra

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Algebra and Trigonometry (MindTap Course List)

Algebra

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:Cengage Learning

SEE MORE TEXTBOOKS

What is a Linear Equation in One Variable?; Author: Don't Memorise;https://www.youtube.com/watch?v=lDOYdBgtnjY;License: Standard YouTube License, CC-BY

Linear Equation | Solving Linear Equations | What is Linear Equation in one variable ?; Author: Najam Academy;https://www.youtube.com/watch?v=tHm3X_Ta_iE;License: Standard YouTube License, CC-BY

Whether the statement “If y 1 and y 2 are solutions of y ″ + y = 0 , then y 1 + y 2 is also a solution of the equation” is true or false.

Solution Summary: The author explains the formula used to determine whether the statement "If y_1 is also a solution of the equation" is true or false.

Concept explainers

Videos

Whether the statement “If y1 and y2 are solutions of y″+y=0 , then y1+y2 is also a solution of the equation” is true or false.

Want to see the full answer?

Chapter 17 Solutions