Homework Help is Here – Start Your Trial Now!
Math
Calculus
(a) For what values of k does the function y = cos(kt) satisfy the differential equation 100y" = -49y? (Enter your answers as a comma-separated list.) 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 100y" = -49y Is equivalent to 100y" + 49y = Thus, LHS = 100y" + 49y= 100(-Ak2 sin(kt) – Bk2 cos(kt)) + = -100AK2 sin(kt) – 100BK2 cos(kt) + sin(kt) + 49B cos(kt) = (49 - 100k2)A sin(kt) + since k2 =

(a) For what values of k does the function y = cos(kt) satisfy the differential equation 100y" = -49y? (Enter your answers as a comma-separated list.) 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 100y" = -49y Is equivalent to 100y" + 49y = Thus, LHS = 100y" + 49y= 100(-Ak2 sin(kt) – Bk2 cos(kt)) + = -100AK2 sin(kt) – 100BK2 cos(kt) + sin(kt) + 49B cos(kt) = (49 - 100k2)A sin(kt) + since k2 =

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
(a) For what values of k does the function y = cos(kt) satisfy the differential equation 100y" = -49y? (Enter your answers as a comma-separated list.) 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 100y" = -49y Is equivalent to 100y" + 49y = Thus, LHS = 100y" + 49y= 100(-Ak2 sin(kt) – Bk2 cos(kt)) + = -100AK2 sin(kt) – 100BK2 cos(kt) + sin(kt) + 49B cos(kt) = (49 - 100k2)A sin(kt) + since k2 =
Transcribed Image Text:(a) For what values of k does the function y = cos(kt) satisfy the differential equation 100y" = -49y? (Enter your answers as a comma-separated list.) 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 100y" = -49y Is equivalent to 100y" + 49y = Thus, LHS = 100y" + 49y= 100(-Ak2 sin(kt) – Bk2 cos(kt)) + = -100AK2 sin(kt) – 100BK2 cos(kt) + sin(kt) + 49B cos(kt) = (49 - 100k2)A sin(kt) + since k2 =
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

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