Homework Help is Here – Start Your Trial Now!
Math
Calculus
11. (16D³ + 12D²2 – 1)y = 0 ; y(0) = 1, y'(0) = 0, y"(0) = –1

11. (16D³ + 12D²2 – 1)y = 0 ; y(0) = 1, y'(0) = 0, y"(0) = –1

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
See similar textbooks
icon
Related questions
Question
Method of Solution 1. Determine the auxiliary equation f (m) = 0 from the given f(D)y = 0. 2. Factor out f(m) = 0 to get the roots m1, m2, m3, ...,Mn. Apply the necessary method in factoring including synthetic division and quadratic formula. 3. Classify each root whether distinct, repeated or imaginary. 4. Formulate the general solution with terms according to the classification of each root m: Distinct: Cremk* for each root mä Repeated: em* (cn-1x"-1 Cn-2x"-2 + ... + c,x + co) for roots m repeated n times Imaginary: eax (c cos bx + c2 sin bx) ах for roots m = a ± bi 5. If indicated, apply the initial condition to get the values of c1, c2, C3, ... , Cn.
Transcribed Image Text:Method of Solution 1. Determine the auxiliary equation f (m) = 0 from the given f(D)y = 0. 2. Factor out f(m) = 0 to get the roots m1, m2, m3, ...,Mn. Apply the necessary method in factoring including synthetic division and quadratic formula. 3. Classify each root whether distinct, repeated or imaginary. 4. Formulate the general solution with terms according to the classification of each root m: Distinct: Cremk* for each root mä Repeated: em* (cn-1x"-1 Cn-2x"-2 + ... + c,x + co) for roots m repeated n times Imaginary: eax (c cos bx + c2 sin bx) ах for roots m = a ± bi 5. If indicated, apply the initial condition to get the values of c1, c2, C3, ... , Cn.
11. (16D³ + 12D²2 – 1)y = 0 ; y(0) = 1, y'(0) = 0, y"(0) = –1
Transcribed Image Text:11. (16D³ + 12D²2 – 1)y = 0 ; y(0) = 1, y'(0) = 0, y"(0) = –1
Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS