Solve the IVPS by the Laplace transform. If necessary, usepartial fraction expansion as in Example 4 of the text. Showall details.1. y' + 5.2y2. у + 2y 3D 0, у(0)3. у" — у' — бу %3D 0, у(0)4. y" + 9y = 10e-t, y(0) = 0, y'(0) = 019.4 sin 2t,y(0) = 01.511, y'(0) = 280, y(0) = 12, y'(0) = 0y(0) = 3.2,5. у"-6. у"бу + 5у — 29 cos 2t,y'(0) = 6.27. y" + 7y' + 12y = 21e", y(0) = 3.5,y' (0)%3D- 108. у"-4y' + 4y = 0, y(0) = 8.1, y' (0) = 3.94y' + 3y9. у"10. y" + 0.04y = 0.02t2, y(0) = -25, y'(0) = 011. y" + 3y' + 2.25y = 9t3 + 64, y(0) = 1,y'(0) = 31.5= 6t – 8, y(0) = 0, y'(0) = 0

(1) Given that y'+5.2y=19.4 sin 2t, y(0)=0 To find the Laplace transform:

Solve the IVPS by the Laplace transform. If necessary, use partial fraction expansion as in Example 4 of the text. Show all details. 1. y' + 5.2y = 19.4 sin 2t, y(0) = 0 2. y' + 2y = 0, y(0) = 1.5 3. у" — у' — бу 3D0, у(0) — 11, 4. у" + 9у %3D 1Ое ", у(0) %3D 0, у'(0) %3D 0 5. у" 6. y" – 6y' + 5y = 29 cos 2t, y(0) y' (0) = 6.2 7. y" + 7y' + 12y = 21e", y(0) = 3.5, y'(0) = - 10 8. y" – 4y' + 4y = 0, y(0) = 8.1, y'(0) = 3.9 9. y" – 4y' + 3y = 10. y" + 0.04y = 0.0212, y(0) = -25, y'(0) = 0 11. y" + 3y' + 2.25y = 9t³ + 64, y(0) = 1, y' (0) = 31.5 y' (0) = 28 10e-t, y(0) = 0, y'(0) = 0 4y = 0, y(0) = 12, y'(0) = 0 = 3.2, 1 | || | || 6t – 8, y(0) = 0, y'(0) = 0 %3D - %3D

Solve the IVPS by the Laplace transform. If necessary, use partial fraction expansion as in Example 4 of the text. Show all details. 1. y' + 5.2y = 19.4 sin 2t, y(0) = 0 2. y' + 2y = 0, y(0) = 1.5 3. у" — у' — бу 3D0, у(0) — 11, 4. у" + 9у %3D 1Ое ", у(0) %3D 0, у'(0) %3D 0 5. у" 6. y" – 6y' + 5y = 29 cos 2t, y(0) y' (0) = 6.2 7. y" + 7y' + 12y = 21e", y(0) = 3.5, y'(0) = - 10 8. y" – 4y' + 4y = 0, y(0) = 8.1, y'(0) = 3.9 9. y" – 4y' + 3y = 10. y" + 0.04y = 0.0212, y(0) = -25, y'(0) = 0 11. y" + 3y' + 2.25y = 9t³ + 64, y(0) = 1, y' (0) = 31.5 y' (0) = 28 10e-t, y(0) = 0, y'(0) = 0 4y = 0, y(0) = 12, y'(0) = 0 = 3.2, 1 | || | || 6t – 8, y(0) = 0, y'(0) = 0 %3D - %3D

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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Question

Solve the IVPS by the Laplace transform. If necessary, use
partial fraction expansion as in Example 4 of the text. Show
all details.
1. y' + 5.2y
2. у + 2y 3D 0, у(0)
3. у" — у' — бу %3D 0, у(0)
4. y" + 9y = 10e-t, y(0) = 0, y'(0) = 0
19.4 sin 2t,
y(0) = 0
1.5
11, y'(0) = 28
0, y(0) = 12, y'(0) = 0
y(0) = 3.2,
5. у"
-
6. у"
бу + 5у — 29 cos 2t,
y'(0) = 6.2
7. y" + 7y' + 12y = 21e", y(0) = 3.5,
y' (0)
%3D
- 10
8. у"
-
4y' + 4y = 0, y(0) = 8.1, y' (0) = 3.9
4y' + 3y
9. у"
10. y" + 0.04y = 0.02t2, y(0) = -25, y'(0) = 0
11. y" + 3y' + 2.25y = 9t3 + 64, y(0) = 1,
y'(0) = 31.5
= 6t – 8, y(0) = 0, y'(0) = 0

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