(a) For what values of k does the function y = cos(kt) satisfy the differential equation 81y" = -64y? (Enter your answers as a comma-separated lis k = (b) For those values of k, verify that every member of the family of functions y = A sin(kt) + B cos(kt) is also a solution. y = A sin(kt) + B cos(kt) y' = Ak cos(kt) – Bk sin(kt) → y" = -Ak² sin(kt) – Bk² cos(kt). The given differential equation 81y" = -64y is equivalent to 81y" + 64y = | Thus, LHS = 81y" + 64y= 81(-Ak2 sin(kt) – Bk² cos(kt)) + 64 = -81AK? sin(kt) – 81BK² cos(kt) + sin(kt) + 64B cos(kt) = (64 – 81k²)A sin(kt) + cos(kt) since k2 =
(a) For what values of k does the function y = cos(kt) satisfy the differential equation 81y" = -64y? (Enter your answers as a comma-separated lis k = (b) For those values of k, verify that every member of the family of functions y = A sin(kt) + B cos(kt) is also a solution. y = A sin(kt) + B cos(kt) y' = Ak cos(kt) – Bk sin(kt) → y" = -Ak² sin(kt) – Bk² cos(kt). The given differential equation 81y" = -64y is equivalent to 81y" + 64y = | Thus, LHS = 81y" + 64y= 81(-Ak2 sin(kt) – Bk² cos(kt)) + 64 = -81AK? sin(kt) – 81BK² cos(kt) + sin(kt) + 64B cos(kt) = (64 – 81k²)A sin(kt) + cos(kt) since k2 =
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...
Related questions
Question
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 3 images
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
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
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
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
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning