Y(t) = (Aot + A₁) sint + (Bot + B₁) cost, provided that sint and cost are not solutions of the homogeneous equation. Problems In each of Problems 1 through 10, find the general solution of the given 15. y" differential equation. In each c Xy"-2y' - 3y = 3e21 2. y" - y' - 2y = -2t+4t² 3. y"+y'-6y = 12e³t + 12e-2t 4. y" - 2y' - 3y = -3te-t 5. y" +2y' = 3 + 4 sin(2t) 6. y" +2y + y = 2e-t 7. y"+y = 3 sin(2t) + t cos(21) 8. u"+wu = cos(wt), w²w² S. u" + w₁u: = cos(wot) 10. y” + y +4y = 2 sinh t Hint: sinht = (e' — e-)/2 In each of Problems 11 through 15, find the solution of the given initial value problem. 11. y"+y' - 2y = 2t, 12. y" + 4y = 1² + 3e', y(0) = 0, y(0) = 0, y(0) = y'(0) = 1 y'(0) = 2 13. y" - 2y + y = te' +4, 1, y'(0) = 1 14. y" + 4y = 3 sin(2t), y(0) = 2, y'(0) = -1 unc N of 16. y 17. y 18. y 19. y 20. y 21. y 22. C from E solution method nonhor where
Y(t) = (Aot + A₁) sint + (Bot + B₁) cost, provided that sint and cost are not solutions of the homogeneous equation. Problems In each of Problems 1 through 10, find the general solution of the given 15. y" differential equation. In each c Xy"-2y' - 3y = 3e21 2. y" - y' - 2y = -2t+4t² 3. y"+y'-6y = 12e³t + 12e-2t 4. y" - 2y' - 3y = -3te-t 5. y" +2y' = 3 + 4 sin(2t) 6. y" +2y + y = 2e-t 7. y"+y = 3 sin(2t) + t cos(21) 8. u"+wu = cos(wt), w²w² S. u" + w₁u: = cos(wot) 10. y” + y +4y = 2 sinh t Hint: sinht = (e' — e-)/2 In each of Problems 11 through 15, find the solution of the given initial value problem. 11. y"+y' - 2y = 2t, 12. y" + 4y = 1² + 3e', y(0) = 0, y(0) = 0, y(0) = y'(0) = 1 y'(0) = 2 13. y" - 2y + y = te' +4, 1, y'(0) = 1 14. y" + 4y = 3 sin(2t), y(0) = 2, y'(0) = -1 unc N of 16. y 17. y 18. y 19. y 20. y 21. y 22. C from E solution method nonhor where
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
5 pl
Transcribed Image Text:Y(t) = (Aot + A₁) sint +(Bot + B₁) cost,
provided that sint and cost are not solutions of the homogeneous equation.
Problems
In each of Problems 1 through 10, find the general solution of the given
differential equation.
Xy"-2y' - 3y = 3e²t
2. y" - y' - 2y = -2t+4t²
3.
4.
5.
6. y" + 2y' + y = 2e¹
7.
y"+y' - 6y = 12e³t + 12e -2t
y" - 2y' - 3y = -3te-t
y" + 2y' = 3 + 4 sin(2t)
y" + y = 3 sin(2t) + t cos(2t)
2
2
8. u" + wu = cos(wt), w² #wo
9. u" + wu = cos(wot)
10. y” +y+4y=2 sinht
In each of Problems 11 through 15, find the solution of the given initial
value problem.
11.
12.
-
Hint: sinht = (e – e )/2
y"+y'-2y = 2t,
y(0) = 0,
y'(0) = 1
y" + 4y = 1² +3e',
y(0) = 0,
y'(0) = 2
13. y" - 2y' + y = te' +4, y(0) = 1, y'(0) = 1
14. y" + 4y = 3 sin(2t),
y(0) = 2, y'(0) = -1
15. y"
In each c
unc
N
of t
16. y"
17. y
18. y'
19. y
20. y
21. y'
22. C
from E
solution
method
nonhor
where
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