Homework Help is Here – Start Your Trial Now!
Math
Calculus
Verify by substitution that the given functions are solutions of the given differential equation. Note that any primes denote derivatives with respect to x. 1 xy" + 15xy' +49y = 0, y₁=71Y2=- In x x What step should you take for each given function to verify that it is a solution to the given differential equation? OA. Substitute the function into the differential equation. O B. Determine the first and second derivatives of the function and substitute into the differential equation. OC. Integrate the function and substitute into the differential equation. O D. Differentiate the function and substitute into the differential equation. Start with y₁= 1 7 X Integrate or differentiate the function as needed. Select the correct choice below and fill in any answer boxes within your choice. OA. The indefinite integral of is fy₁ dx= "' = and the second derivative is y₁' OB. The first derivative is y₁' = OC. The first derivative is y₁ OD. The function does not need to be integrated or differentiated to verify that it is a solution to the differential equation.

Verify by substitution that the given functions are solutions of the given differential equation. Note that any primes denote derivatives with respect to x. 1 xy" + 15xy' +49y = 0, y₁=71Y2=- In x x What step should you take for each given function to verify that it is a solution to the given differential equation? OA. Substitute the function into the differential equation. O B. Determine the first and second derivatives of the function and substitute into the differential equation. OC. Integrate the function and substitute into the differential equation. O D. Differentiate the function and substitute into the differential equation. Start with y₁= 1 7 X Integrate or differentiate the function as needed. Select the correct choice below and fill in any answer boxes within your choice. OA. The indefinite integral of is fy₁ dx= "' = and the second derivative is y₁' OB. The first derivative is y₁' = OC. The first derivative is y₁ OD. The function does not need to be integrated or differentiated to verify that it is a solution to the differential equation.

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
Verify by substitution that the given functions are solutions of the given differential equation. Note that any primes denote derivatives with respect to x. 1 In x x²y" + 15xy' +49y = 0, y₁ = 7.Y₂ = X What step should you take for each given function to verify that it is a solution to the given differential equation? O A. Substitute the function into the differential equation. OB. Determine the first and second derivatives of the function and substitute into the differential equation. OC. Integrate the function and substitute into the differential equation. O D. Differentiate the function and substitute into the differential equation. 1 Start with y₁= Integrate or differentiate the function as needed. Select the correct choice below and fill in any answer boxes within your choice. X Sy₁ dx OA. The indefinite integral of is OB. The first derivative is y,' = OC. The first derivative is y₁' OD. The function does not need to be integrated or differentiated to verify that it is a solution to the differential equation. = "1- and the second derivative is y₁"
Transcribed Image Text:Verify by substitution that the given functions are solutions of the given differential equation. Note that any primes denote derivatives with respect to x. 1 In x x²y" + 15xy' +49y = 0, y₁ = 7.Y₂ = X What step should you take for each given function to verify that it is a solution to the given differential equation? O A. Substitute the function into the differential equation. OB. Determine the first and second derivatives of the function and substitute into the differential equation. OC. Integrate the function and substitute into the differential equation. O D. Differentiate the function and substitute into the differential equation. 1 Start with y₁= Integrate or differentiate the function as needed. Select the correct choice below and fill in any answer boxes within your choice. X Sy₁ dx OA. The indefinite integral of is OB. The first derivative is y,' = OC. The first derivative is y₁' OD. The function does not need to be integrated or differentiated to verify that it is a solution to the differential equation. = "1- and the second derivative is y₁"
Substitute the appropriate expressions into the differential equation. 2 +15x+49(=0 (Type the terms of your expression in the same order as they appear in the original expression.) 1 2 How can this result be used to verify that y₁= is a solution of xy" + 15xy' +49y=0? 7 X 1 O A. Differentiating the resulting equation with respect to x gives 0 = 0, so y₁= is a solution to the differential equation. X 1 OB. Simplifying the left side gives the equation 0 = 0, which means y₁= is a solution to the differential equation. 7 = OC. There are no values of x that satisfy the resulting equation, which means that y₁ 1 is a solution to the differential equation. X A 1 O D. Solving this equation gives x = 0, which means y₁ = is a solution to the differential equation. X
Transcribed Image Text:Substitute the appropriate expressions into the differential equation. 2 +15x+49(=0 (Type the terms of your expression in the same order as they appear in the original expression.) 1 2 How can this result be used to verify that y₁= is a solution of xy" + 15xy' +49y=0? 7 X 1 O A. Differentiating the resulting equation with respect to x gives 0 = 0, so y₁= is a solution to the differential equation. X 1 OB. Simplifying the left side gives the equation 0 = 0, which means y₁= is a solution to the differential equation. 7 = OC. There are no values of x that satisfy the resulting equation, which means that y₁ 1 is a solution to the differential equation. X A 1 O D. Solving this equation gives x = 0, which means y₁ = is a solution to the differential equation. X
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 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