The method of reduction of order (Section 3.4) can also be used for the nonhomogeneous equation y" +p(t)y' + q(t)y = g(). (38) provided one solution y of the corresponding homogeneous equation is known. Let y= ()y() and show that y satisfies equation 38 if v is a solution of yı(" + (2y,) + p(t)y = g(0). (39) Equation 39 is a first-order linear differential equation for v. By solving equation 39 for v, integrating the result to find v, and then multiplying by y1(O. you can find the general solution of equation 38. This method simultaneously finds both the second homogeneous solution and a particular solution. Use the method above to solve the differential equation ty" – (1+t)y' +y = 5t2e24, t > 0, y (t) = 1+ t. Use C1, C2, ... for the constants of integration.
The method of reduction of order (Section 3.4) can also be used for the nonhomogeneous equation y" +p(t)y' + q(t)y = g(). (38) provided one solution y of the corresponding homogeneous equation is known. Let y= ()y() and show that y satisfies equation 38 if v is a solution of yı(" + (2y,) + p(t)y = g(0). (39) Equation 39 is a first-order linear differential equation for v. By solving equation 39 for v, integrating the result to find v, and then multiplying by y1(O. you can find the general solution of equation 38. This method simultaneously finds both the second homogeneous solution and a particular solution. Use the method above to solve the differential equation ty" – (1+t)y' +y = 5t2e24, t > 0, y (t) = 1+ t. Use C1, C2, ... for the constants of integration.
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
![The method of reduction of order (Section 3.4) can also be used for the nonhomogeneous equation
y" +p(t)y' + g{t}y = g(t).
(38)
provided one solution yı of the corresponding homogeneous equation is known. Let y = r(t)y) and show
that y satisfies equation 38 if v is a solution of
y1(O" + (2y, ) + plt)yO = g(0).
(39)
Equation 39 is a first-order linear differential equation for r'. By solving equation 39 for v, integrating the
result to find v, and then multiplying by y1(O. you can find the general solution of equation 38. This method
simultaneously finds both the second homogeneous solution and a particular solution.
Use the method above to solve the differential equation
ty" – (1+t)y' +y = 5t°e, t > 0, y1 (t) = 1+t.
Use C1, C2, ... for the constants of integration.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffc262d38-8642-4292-8f86-e10c24c29ddb%2F6190ea3a-9ec8-4fc6-8794-b841c48201a7%2Fjadnzk8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The method of reduction of order (Section 3.4) can also be used for the nonhomogeneous equation
y" +p(t)y' + g{t}y = g(t).
(38)
provided one solution yı of the corresponding homogeneous equation is known. Let y = r(t)y) and show
that y satisfies equation 38 if v is a solution of
y1(O" + (2y, ) + plt)yO = g(0).
(39)
Equation 39 is a first-order linear differential equation for r'. By solving equation 39 for v, integrating the
result to find v, and then multiplying by y1(O. you can find the general solution of equation 38. This method
simultaneously finds both the second homogeneous solution and a particular solution.
Use the method above to solve the differential equation
ty" – (1+t)y' +y = 5t°e, t > 0, y1 (t) = 1+t.
Use C1, C2, ... for the constants of integration.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
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 4 steps with 3 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.Recommended textbooks for you
![Calculus: Early Transcendentals](https://www.bartleby.com/isbn_cover_images/9781285741550/9781285741550_smallCoverImage.gif)
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
![Thomas' Calculus (14th Edition)](https://www.bartleby.com/isbn_cover_images/9780134438986/9780134438986_smallCoverImage.gif)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
![Calculus: Early Transcendentals (3rd Edition)](https://www.bartleby.com/isbn_cover_images/9780134763644/9780134763644_smallCoverImage.gif)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
![Calculus: Early Transcendentals](https://www.bartleby.com/isbn_cover_images/9781285741550/9781285741550_smallCoverImage.gif)
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
![Thomas' Calculus (14th Edition)](https://www.bartleby.com/isbn_cover_images/9780134438986/9780134438986_smallCoverImage.gif)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
![Calculus: Early Transcendentals (3rd Edition)](https://www.bartleby.com/isbn_cover_images/9780134763644/9780134763644_smallCoverImage.gif)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
![Calculus: Early Transcendentals](https://www.bartleby.com/isbn_cover_images/9781319050740/9781319050740_smallCoverImage.gif)
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
![Precalculus](https://www.bartleby.com/isbn_cover_images/9780135189405/9780135189405_smallCoverImage.gif)
![Calculus: Early Transcendental Functions](https://www.bartleby.com/isbn_cover_images/9781337552516/9781337552516_smallCoverImage.gif)
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning