11. x' = y, y'= -x 12. x' = y, y'=x 13. x'= -2y, y'= 2x; x (0) = 1, y(0) = 0 14. x' = 10y, y'= -10x; x(0) = 3, y(0) = 4 15. x'= y, y'= -8x 16. x' = 8y, y'= -2x
11. x' = y, y'= -x 12. x' = y, y'=x 13. x'= -2y, y'= 2x; x (0) = 1, y(0) = 0 14. x' = 10y, y'= -10x; x(0) = 3, y(0) = 4 15. x'= y, y'= -8x 16. x' = 8y, y'= -2x
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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Can anyone help me # 12 and 14
![Use the method of Examples 5, 6, and 7 to find general solu-
tions of the systems in Problems 11 through 20. If initial con-
ditions are given, find the corresponding particular solution.
For each problem, use a computer system or graphing calcu-
lator to construct a direction field and typical solution curves
for the given system.
11. x' = y, y'= -x
12. x' = y, y' = x
13. x' = -2y, y' = 2x; x (0) = 1,
14. x' =
15. x' =
16. x' = 8y, y'= -2x
17. x' = y, y' = 6x = y; x(0) = 1, y (0) = 2
18. x'=-y, y'= 10x - 7y; x(0) = 2, y(0) = -7
19. x'=-y, y'= 13x + 4y; x(0) = 0, y(0) = 3
20. x' = y, y'= -9x + 6y
21. (a) Calculate [x(1)]²+ [y(1)]² to show that the trajecto-
ries of the system x' = y, y'= -x of Problem 11 are
circles. (b) Calculate [x()]² - [y(t)]² to show that the
trajectories of the system x' = y, y' = x of Problem 12
are hyperbolas.
y(0) = 0
10y, y'= -10x; x(0) = 3, y (0) = 4
y, y'= -8x](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3f6c81c7-9a41-4014-8916-60df888d5014%2Fb14b7e98-65ba-443a-a175-65e3e8cc934c%2F07yxxe_processed.png&w=3840&q=75)
Transcribed Image Text:Use the method of Examples 5, 6, and 7 to find general solu-
tions of the systems in Problems 11 through 20. If initial con-
ditions are given, find the corresponding particular solution.
For each problem, use a computer system or graphing calcu-
lator to construct a direction field and typical solution curves
for the given system.
11. x' = y, y'= -x
12. x' = y, y' = x
13. x' = -2y, y' = 2x; x (0) = 1,
14. x' =
15. x' =
16. x' = 8y, y'= -2x
17. x' = y, y' = 6x = y; x(0) = 1, y (0) = 2
18. x'=-y, y'= 10x - 7y; x(0) = 2, y(0) = -7
19. x'=-y, y'= 13x + 4y; x(0) = 0, y(0) = 3
20. x' = y, y'= -9x + 6y
21. (a) Calculate [x(1)]²+ [y(1)]² to show that the trajecto-
ries of the system x' = y, y'= -x of Problem 11 are
circles. (b) Calculate [x()]² - [y(t)]² to show that the
trajectories of the system x' = y, y' = x of Problem 12
are hyperbolas.
y(0) = 0
10y, y'= -10x; x(0) = 3, y (0) = 4
y, y'= -8x
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