21. у" — 4y' + Зу %3D 0; у (0) %3D 7, у'(0) 3 11 22. 9y" + бу' + 4у %3 0;B у (0) — 3, у' (0) — 4 23. у" — бу' + 25у %3D 0;B у (0) — 3, у'(0) — 1 (3)
21. у" — 4y' + Зу %3D 0; у (0) %3D 7, у'(0) 3 11 22. 9y" + бу' + 4у %3 0;B у (0) — 3, у' (0) — 4 23. у" — бу' + 25у %3D 0;B у (0) — 3, у'(0) — 1 (3)
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
Need help for # 21 and 23
Transcribed Image Text:(С8 COS 3x + с9 sin 3x) + хе** (с10 сos Зх + с11 sin 3x).
3.3 Problems
Find the general solutions of the differential equations in Prob-
lems 1 through 20.
19. у(3) + у" -у' — у %3D 0
20. y(4) + 2y(3) + 3y" + 2y' + y = 0 (Suggestion: Expand
(r2 + r + 1)2.)
1. y" – 4y = 0
3. у" + Зу' — 10у 3D 0
5. y" + 6y' + 9y = 0
7. 4y" – 12y' + 9y = 0
9. y" + 8y' + 25y = 0
11. у(4) — 8y(3) + 16у" — 0
12. y(4) – 3y(3) + 3y" – y' = 0
13. 9y(3) + 12y" + 4y' = 0
15. y(4) – 8y" + 16y = 0
17. 6y(4) + 11y" + 4y = 0
//
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2. 2y" - Зу' — о
4. 2y" – 7y' + 3y = 0
6. y" + 5y' + 5y = 0
8. у" — бу' + 13у 3D 0
10. 5y(4) + Зу(3) — 0
Solve the initial value problems given in Problems 21 through
26.
||
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21. y" – 4y' + 3y = 0; y(0) = 7, y'(0) = 11
22. 9y" + 6y' + 4y = 0; y(0) = 3, y'(0) = 4
23. у" — бу' + 25у 3D 0%;B у (0) — 3, у' (0) 3D 1
24. 2у(3) — Зу" - 2у' %3D 0%; у (0) %3D 1, у' (0) %3D —1, у" (0) — 3
25. 3y(3) + 2y" = 0; y(0) = -1, y'(0) = 0, y"(0) = 1
26. у (3) + 10y" + 25y' %3D 0%;B у (0) %3 3, у' (0) %3 4, у" (О) %3D 5
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14. y(4) + 3y" – 4y = 0
16. у (4)
18. у (4)
-1, y" (0) = 3
+ 18y" + 81y = 0
= 16y
-
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