In Problems 1-36 find the gel 1. 4y" + y = 0 3. y" - 36y = 0 5. y" +9y = 0 7. y" - y' - 6y = 0 d²y dx² 9. 29. + 8- 11. y" + 3y' - 5y = 0 13. 12y" - 5y' - 2y = 0 15. y" - 4y' + 5y = 0 17. 3y" + 2y' + y = 0 19. y4y" - 5y' = 0 21. y" - y = 0 23. y" - 5y" + 3y' + 9y = 0 25. y"+y" - 2y = 0 27. y"" + 3y" + 3y' + y = 0 d'y d'y d'y + + dx4 dx³ dx² d'y 31. 16- dx4 d'y 33. dy dx - + 16y = 0 + 24 16- d'y dx² dy = 0 = + 9y = 0 2. 2y" - 5y' = 0 4. y" - 8y = 0 6. 3y" + y = 0 8. y" - 3y d²y dx² 10. - 30. 10 32. 12. y" + 4y' - y = 0 14. 8y" + 2y' - y = 0 16. 2y" - 3y + 4y = 0 18. 2y" + 2y + y = 0 20. 4y" + 4y" + y' = 0 d'y dx4 d'y 22. y" + 5y" = 0 24. y" + 3y" - 4y' 12y = C + 2y = 0 dy - dx 26. y" - y" - 4y = 0 28. y" - 6y" + 12y' - 8y = C d'y d²y dx4 dx² d²y dx² d'y - 2 + 25y = 0 - 7 - + y = 0 - 18y = 0 d'y
In Problems 1-36 find the gel 1. 4y" + y = 0 3. y" - 36y = 0 5. y" +9y = 0 7. y" - y' - 6y = 0 d²y dx² 9. 29. + 8- 11. y" + 3y' - 5y = 0 13. 12y" - 5y' - 2y = 0 15. y" - 4y' + 5y = 0 17. 3y" + 2y' + y = 0 19. y4y" - 5y' = 0 21. y" - y = 0 23. y" - 5y" + 3y' + 9y = 0 25. y"+y" - 2y = 0 27. y"" + 3y" + 3y' + y = 0 d'y d'y d'y + + dx4 dx³ dx² d'y 31. 16- dx4 d'y 33. dy dx - + 16y = 0 + 24 16- d'y dx² dy = 0 = + 9y = 0 2. 2y" - 5y' = 0 4. y" - 8y = 0 6. 3y" + y = 0 8. y" - 3y d²y dx² 10. - 30. 10 32. 12. y" + 4y' - y = 0 14. 8y" + 2y' - y = 0 16. 2y" - 3y + 4y = 0 18. 2y" + 2y + y = 0 20. 4y" + 4y" + y' = 0 d'y dx4 d'y 22. y" + 5y" = 0 24. y" + 3y" - 4y' 12y = C + 2y = 0 dy - dx 26. y" - y" - 4y = 0 28. y" - 6y" + 12y' - 8y = C d'y d²y dx4 dx² d²y dx² d'y - 2 + 25y = 0 - 7 - + y = 0 - 18y = 0 d'y
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 someone help me answer 5 and 7
Transcribed Image Text:Answers to odd-numbered problems begin on page A-8.
In Problems 1-36 find the general solution of the given differential equation.
1. 4y" + y' = 0
2. 2y" - 5y' = 0
3. y" - 36y = 0
4. y" - 8y = 0
5. y" + 9y = 0
6. 3y" + y = 0
7. y" - y' - 6y = 0
8. y" - 3y' + 2y = 0
d²y dy
d²y
dx²
dx²
9.
11. y" + 3y' - 5y = 0
13. 12y" - 5y' - 2y = 0
15. y" - 4y' + 5y = 0
17. 3y" + 2y' + y = 0
19. y" - 4y" - 5y' = 0
21. y" - y = 0
23. y" - 5y" + 3y' + 9y = 0
25. y""+y" - 2y = 0
27. y" + 3y" + 3y' + y = 0
d'y d'y
d'y
+
+
dx³ dx²
= 0
dx4
d'y
dx²
29.
31. 16
33.
dy
+ 8- + 16y = 0
dx
35.
d'y
dx4
d'y
dxs
d'y
dx5
+ 24
16
+ 5
dy
dx
d'y
dx4
=
+9y = 0
0
2
d³y
dx³
10
10.
12. y" + 4y' - y = 0
14. 8y" + 2y' - y = 0
16. 2y" - 3y + 4y = 0
18. 2y" + 2y' + y = 0
20. 4y" + 4y" + y' = 0
30.
32.
22. y" + 5y" = 0
24. y" + 3y" - 4y' - 12y = 0
26. y"" - y" - 4y = 0
28. y" - 6y" + 12y' - 8y = 0
d'y
dx4
34.
-
d'y dy
+
dx²
dx
10 + 25y = 0
dx
d'y
dx4
d'y
dxs
-2
- 7
2
+ 5y = 0
d²y
dx²
d²y
dx²
d'y
dx4
+ y = 0
TOPP
18y = 0
d'y
dx³
+ 17
=
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