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Find general solutions in powers of x of the differential equa- tions in Problems 1 through 15. State the recurrence relation and the guaranteed radius of convergence in each case. 1. (x2 - 1)y" + 4xy' + 2y = 0 2. (x2 + 2)y" + 4xy' + 2y 0 3. y" + xy' + y = 0 4. (x2 + 1)y" + 6xy' +4y 0 5. (x2 - 3)y" + 2xy' 0 7. (x+3)y 8. (2 x)y" - xy' + 16y = 0 9. (x2 – 1)y" + 8xy+ 12y =0 10. 3y" + xy' – 4y = 0 11. 5y" – 2xy + 10y = 0 12. y" – x?y' – 3xy = 0 13. y" +x'y' + 2ry 0 14. y" + xy = 0 (an Airy equation) 15. y" +x²y = 0 %3D | Exu' t 12y = 0

Find general solutions in powers of x of the differential equa- tions in Problems 1 through 15. State the recurrence relation and the guaranteed radius of convergence in each case. 1. (x2 - 1)y" + 4xy' + 2y = 0 2. (x2 + 2)y" + 4xy' + 2y 0 3. y" + xy' + y = 0 4. (x2 + 1)y" + 6xy' +4y 0 5. (x2 - 3)y" + 2xy' 0 7. (x+3)y 8. (2 x)y" - xy' + 16y = 0 9. (x2 – 1)y" + 8xy+ 12y =0 10. 3y" + xy' – 4y = 0 11. 5y" – 2xy + 10y = 0 12. y" – x?y' – 3xy = 0 13. y" +x'y' + 2ry 0 14. y" + xy = 0 (an Airy equation) 15. y" +x²y = 0 %3D | Exu' t 12y = 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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Find general solutions in powers of x of the differential equa- tions in Problems 1 through 15. State the recurrence relation and the guaranteed radius of convergence in each case. 7. (x +3)y" - 7xy + 16y = 0 8. (2 - x')y" - xy' + 16y = 0 9. (x2 - 1)y" + 8xy +12y = 0 10. 3y" +xy - 4y = 0 11. 5y" – 2xy+ 10y = 0 12. y- x'y' - 3xy = 0 13. y +x'y' + 2xy = 0 14. y" + xy = 0 (an Airy equation) 15. y" +x'y = 0 %3D 1. (x2 - 1)y" + 4xy' + 2y = 0 2. (x2 + 2)y" + 4xy' + 2y = 0 3. y" + xy' +y = 0 4. (x2 + 1)y" + 6xy' + 4y = 0 5. (x2 - 3)y" + 2xy' = 0 1) y" 6. (x2 – – = 0 6xy' + 12y
Transcribed Image Text:Find general solutions in powers of x of the differential equa- tions in Problems 1 through 15. State the recurrence relation and the guaranteed radius of convergence in each case. 7. (x +3)y" - 7xy + 16y = 0 8. (2 - x')y" - xy' + 16y = 0 9. (x2 - 1)y" + 8xy +12y = 0 10. 3y" +xy - 4y = 0 11. 5y" – 2xy+ 10y = 0 12. y- x'y' - 3xy = 0 13. y +x'y' + 2xy = 0 14. y" + xy = 0 (an Airy equation) 15. y" +x'y = 0 %3D 1. (x2 - 1)y" + 4xy' + 2y = 0 2. (x2 + 2)y" + 4xy' + 2y = 0 3. y" + xy' +y = 0 4. (x2 + 1)y" + 6xy' + 4y = 0 5. (x2 - 3)y" + 2xy' = 0 1) y" 6. (x2 – – = 0 6xy' + 12y
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