Verify that the indicated function is an explicit solution of the given differential equation. Assume an appropriate interval I of definition for each solution. y" – 6y' + 25y = 0; y = e3x cos 4x When y = ex cos 4x, y' = y" = Thus, in terms of x, у" - бу" + 25у 3D + 25 e3x cos 4x
Verify that the indicated function is an explicit solution of the given differential equation. Assume an appropriate interval I of definition for each solution. y" – 6y' + 25y = 0; y = e3x cos 4x When y = ex cos 4x, y' = y" = Thus, in terms of x, у" - бу" + 25у 3D + 25 e3x cos 4x
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
Transcribed Image Text:Verify that the indicated function is an explicit solution of the given differential equation. Assume an appropriate interval I of definition for each solution.
у" - бу' + 25у %3D 0;
y = e3x cos 4x
When y = e3X cos 4x,
y'
=
y" =
Thus, in terms of x,
у" — бу' + 25у 3D
+ 25 e3x cos 4x
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps
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