5. (x2 - 3)y" + 2xy' = 0
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Number 5
![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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F40174750-f49c-418a-99e5-b99a47847661%2F4e3b31c5-8882-4550-a399-b7fc1ed7b582%2Fwmv6l2w_processed.jpeg&w=3840&q=75)
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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