= 0 = 0 - = 0 2. 2y" - Зу' %3D 0 4. 2y" - 7у' + Зу %3D 0 6. у" + 5y' + 5у %3D 0 8. у" — бу' + 13у %3D 0 10. 5у(4) + 3у(3) — 0 = 0 6y" = 0 y" – y' = 0 4y' = 0 y = 0 4y = 0 14. у (4) + Зу" —- 4у 3D 0 16. у (4) + 18у"+ 81у %3D0 18. у(4) —D 16у %3D
= 0 = 0 - = 0 2. 2y" - Зу' %3D 0 4. 2y" - 7у' + Зу %3D 0 6. у" + 5y' + 5у %3D 0 8. у" — бу' + 13у %3D 0 10. 5у(4) + 3у(3) — 0 = 0 6y" = 0 y" – y' = 0 4y' = 0 y = 0 4y = 0 14. у (4) + Зу" —- 4у 3D 0 16. у (4) + 18у"+ 81у %3D0 18. у(4) —D 16у %3D
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 please for # 15
Transcribed Image Text:### 3.3 Problems
**Find the general solutions of the differential equations in Problems 1 through 20.**
1. \( y'' - 4y = 0 \)
2. \( 2y'' - 3y' = 0 \)
3. \( y'' + 3y' - 10y = 0 \)
4. \( 2y'' - 7y' + 3y = 0 \)
5. \( y'' + 6y' + 9y = 0 \)
6. \( y'' + 5y' + 5y = 0 \)
7. \( 4y'' - 12y' + 9y = 0 \)
8. \( y'' - 6y' + 13y = 0 \)
9. \( y'' + 8y' + 25y = 0 \)
10. \( 5y^{(4)} + 3y^{(3)} = 0 \)
11. \( y^{(4)} - 8y^{(3)} + 16y'' = 0 \)
12. \( y^{(4)} - 3y^{(3)} + 3y'' - y' = 0 \)
13. \( 9y^{(3)} + 12y'' + 4y' = 0 \)
14. \( y^{(4)} + 3y'' - 4y = 0 \)
15. \( y^{(4)} - 8y'' + 16y = 0 \)
16. \( 4y^{(4)} + 18y''' + 81y = 0 \)
17. \( 6y^{(4)} + 11y'' + 4y = 0 \)
18. \( y^{(4)} = 16y \)
19. \( y^{(3)} + y'' - y' - y = 0 \)
20. \( y^{(4)} + 2y^{(3)} + 3y'' + 2y' + y = 0 \) (Suggestion: Expand \( (r^2 + r + 1)^2 \).)
**Solve the initial value problems given in Problems 21 through 26.**
21. \( y'' - 4y
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Given differential equation has constant cofficient so We can solve by auxillary equation.
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