Number 15 pratice problems ### Chapter 6: Series Solutions of Linear Equations#### In Problems 7–18, find two power series solutions of the given differential equation about the ordinary point $ x = 0 $.7. $ y'' + xy = 0 $8. $ y'' + xy' = 0 $9. $ y'' - 2xy' + y = 0 $10. $ y'' xy' + 2y = 0 $11. $ y'' + x^2y' + xy = 0 $12. $ y'' + 2xy' + 2y = 0 $13. $ (x - 1)y'' + y' = 0 $14. $ (x + 2)y'' + xy' - y = 0 $15. $ (x - 1)y'' + 2xy' - y = 0 $16. $ (x - 2)y'' - 6y = 0 $17. $ (x^2 + 2)y'' + 3xy' - y = 0 $18. $ (x^2 - 1)y'' + xy' - y = 0 $#### In Problems 19–22, use the power series method to solve the given initial-value problem.19. $ (x - 1)y'' - xy' + y = 0 $, $ y(0) = 2 $, $ y'(0) = 6 $20. $ (x + 1)y'' -(2 - x)y' + y = 0 $, $ y(0) = 2 $, $ y'(0) = -1 $21. $ y'' - 2xy'' + 8y = 0 $, $ y(0) = 3 $, $ y'(0) = 0 $22. $ (x - 1)y'' + 2xy' = 0 $, $ y(0) = 0 $, $ y'(0) = 1 $#### In Problems 23 and 24, use the procedure in Example 8 to find two power series solutions of the given differential equation about the ordinary point $ x = 0 $.*Note: Example 8 from the referenced textbook is not provided here.*#### Computer Lab

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Description: Number 15 pratice problems ### Chapter 6: Series Solutions of Linear Equations#### In Problems 7–18, find two power series solutions of the given differential equation about the ordinary point $ x = 0 $.7. $ y'' + xy = 0 $8. $ y'' + xy' = 0 $9.

The equation is y’’ – (x + 1) y’ – y = 0

Answered: y-(x+1)y'-y=0

Math

Advanced Math

y-(x+1)y'-y=0

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Binomial Distribution

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Question

Number 15 pratice problems

### Chapter 6: Series Solutions of Linear Equations

#### In Problems 7–18, find two power series solutions of the given differential equation about the ordinary point $ x = 0 $.

7. $ y'' + xy = 0 $

8. $ y'' + xy' = 0 $

9. $ y'' - 2xy' + y = 0 $

10. $ y'' xy' + 2y = 0 $

11. $ y'' + x^2y' + xy = 0 $

12. $ y'' + 2xy' + 2y = 0 $

13. $ (x - 1)y'' + y' = 0 $

14. $ (x + 2)y'' + xy' - y = 0 $

15. $ (x - 1)y'' + 2xy' - y = 0 $

16. $ (x - 2)y'' - 6y = 0 $

17. $ (x^2 + 2)y'' + 3xy' - y = 0 $

18. $ (x^2 - 1)y'' + xy' - y = 0 $

#### In Problems 19–22, use the power series method to solve the given initial-value problem.

19. $ (x - 1)y'' - xy' + y = 0 $, $ y(0) = 2 $, $ y'(0) = 6 $

20. $ (x + 1)y'' -(2 - x)y' + y = 0 $, $ y(0) = 2 $, $ y'(0) = -1 $

21. $ y'' - 2xy'' + 8y = 0 $, $ y(0) = 3 $, $ y'(0) = 0 $

22. $ (x - 1)y'' + 2xy' = 0 $, $ y(0) = 0 $, $ y'(0) = 1 $

#### In Problems 23 and 24, use the procedure in Example 8 to find two power series solutions of the given differential equation about the ordinary point $ x = 0 $.

*Note: Example 8 from the referenced textbook is not provided here.*

#### Computer Lab

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