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
17
![**Title: Variation of Parameters for Particular Solutions**
**Instructions:**
In Exercises 7–29, use variation of parameters to find a particular solution, given the solutions \( y_1, y_2 \) of the complementary equation.
1. **Exercise 7:**
\[
x^2y'' + xy' - y = 2x^2 + 2; \quad y_1 = x, \quad y_2 = \frac{1}{x}
\]
2. **Exercise 8:**
\[
xy'' + (2 - 2x)y' + (x - 2)y = e^{2x}; \quad y_1 = e^x, \quad y_2 = \frac{e^x}{x}
\]
3. **Exercise 9:**
\[
4x^2y'' + (4x - 8x^2)y' + (4x^2 - 4x - 1)y = 4x^{1/2} e^x, \quad x > 0; \quad y_1 = x^{1/2}e^x, \quad y_2 = x^{-1/2}e^x
\]
4. **Exercise 10:**
\[
y'' + 4xy' + (4x^2 + 2)y = 4e^{-x(x+2)}; \quad y_1 = e^{-x^2}, \quad y_2 = xe^{-x^2}
\]
5. **Exercise 11:**
\[
x^2y'' - 4xy' + 6y = x^{5/2}, \quad x > 0; \quad y_1 = x^2, \quad y_2 = x^3
\]
6. **Exercise 12:**
\[
x^2y'' - 3xy' + 3y = 2x^4 \sin x; \quad y_1 = x, \quad y_2 = x^3
\]
7. **Exercise 13:**
\[
(2x + 1)y' - 2y - (2x + 3)y = (2x + 1)^2 e^{-x](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff57c5c9b-acb3-4a3d-a39b-55eeff7ee4ad%2Fc875c09e-0fee-4e81-9232-840d5c57cd10%2Fysmtke4_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Variation of Parameters for Particular Solutions**
**Instructions:**
In Exercises 7–29, use variation of parameters to find a particular solution, given the solutions \( y_1, y_2 \) of the complementary equation.
1. **Exercise 7:**
\[
x^2y'' + xy' - y = 2x^2 + 2; \quad y_1 = x, \quad y_2 = \frac{1}{x}
\]
2. **Exercise 8:**
\[
xy'' + (2 - 2x)y' + (x - 2)y = e^{2x}; \quad y_1 = e^x, \quad y_2 = \frac{e^x}{x}
\]
3. **Exercise 9:**
\[
4x^2y'' + (4x - 8x^2)y' + (4x^2 - 4x - 1)y = 4x^{1/2} e^x, \quad x > 0; \quad y_1 = x^{1/2}e^x, \quad y_2 = x^{-1/2}e^x
\]
4. **Exercise 10:**
\[
y'' + 4xy' + (4x^2 + 2)y = 4e^{-x(x+2)}; \quad y_1 = e^{-x^2}, \quad y_2 = xe^{-x^2}
\]
5. **Exercise 11:**
\[
x^2y'' - 4xy' + 6y = x^{5/2}, \quad x > 0; \quad y_1 = x^2, \quad y_2 = x^3
\]
6. **Exercise 12:**
\[
x^2y'' - 3xy' + 3y = 2x^4 \sin x; \quad y_1 = x, \quad y_2 = x^3
\]
7. **Exercise 13:**
\[
(2x + 1)y' - 2y - (2x + 3)y = (2x + 1)^2 e^{-x
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 2 steps with 2 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