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9. 9y" - 12y' + 4y = 0, y(0) = 2, y'(0) = -1 10. 0 61² +9 O O (0)

9. 9y" - 12y' + 4y = 0, y(0) = 2, y'(0) = -1 10. 0 61² +9 O O (0)

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...
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Question

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Problems m In each of Problems 1 through 8, find the general solution of the given differential equation. Broopa lanis y" - 2y + y = 0 9y" + 6y' + y = 0 4y" - 4y' - 3y = 0 y" - 2y' +10y = 0 y"-6y' +9y = 0 4y" +17y' + 4y = 0 16y" +24y' +9y = 0 1. 2. 3. 4. $1 notisupen 5. 6. 7. 8. 2y" +2y + y = 0 In each of Problems 9 through 11, solve the given initial value problem. Sketch the graph of the solution and describe its behavior for increasing t. 9. 9y" - 12y' + 4y = 0, y" - 6y' +9y = 0, y" +4y' + 4y = 0, MUS y(0) = 2, y'(0) = -1 y(0) = 0, y'(0) = 2 y(-1) = 2, y'(-1) = 1 10. 11. 12. Consider the following modification of the initial value problem in Example 2: ²/ y" - y' + = 0, y(0) = 2, y'(0) = b. Find the solution as a function of b, and then determine the critical value of b that separates solutions that remain positive for all t> 0 from those that eventually become negative. N 14. cor the the Pro so 15
Transcribed Image Text:Problems m In each of Problems 1 through 8, find the general solution of the given differential equation. Broopa lanis y" - 2y + y = 0 9y" + 6y' + y = 0 4y" - 4y' - 3y = 0 y" - 2y' +10y = 0 y"-6y' +9y = 0 4y" +17y' + 4y = 0 16y" +24y' +9y = 0 1. 2. 3. 4. $1 notisupen 5. 6. 7. 8. 2y" +2y + y = 0 In each of Problems 9 through 11, solve the given initial value problem. Sketch the graph of the solution and describe its behavior for increasing t. 9. 9y" - 12y' + 4y = 0, y" - 6y' +9y = 0, y" +4y' + 4y = 0, MUS y(0) = 2, y'(0) = -1 y(0) = 0, y'(0) = 2 y(-1) = 2, y'(-1) = 1 10. 11. 12. Consider the following modification of the initial value problem in Example 2: ²/ y" - y' + = 0, y(0) = 2, y'(0) = b. Find the solution as a function of b, and then determine the critical value of b that separates solutions that remain positive for all t> 0 from those that eventually become negative. N 14. cor the the Pro so 15
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