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Please show all work and do all parts. Only do question 1.

Please show all work and do all parts. Only do question 1.

Advanced Engineering Mathematics
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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Please show all work and do all parts. Only do question 1.
-√2 + √2 -√2-√2 1. y" - 4y = 0 4. 16y(4) - 8y"+y=0 √2+√2 √2-1√2 FIGURE 3.20 The four roots of 24 + 16 = 0 lie on a circle of radius 16¹/4 = 2 and have an Eulbus angular separation of 2π/4 = π/2 radians. The roots occur in two complex conjugate pairs. Exercises 1-18: In each exercise, (a) Find the general solution of the differential equation. (b) If initial conditions are specified, solve the initial value problem. Re 2. y"+y" - y - y = 0 5. 16y (4) + 8y"+y = 0 8. y(4)-y=0 7. y" - 2y" - y' + 2y = 0 10. 2y" - y" = 0 11. y" + y = 0 13. y) - y = 0 14. y(4) - y""+y'- y = 0 15. y" + 2y" + y = 0, y(0) = 0, y'(0) = 0, y'(0) = 1 3. y""+y" + 4y + 4y = 0 6. y" - y = 0 9. y"" + 8y = 0 12. y(4) + 2y" + y = 0
Transcribed Image Text:-√2 + √2 -√2-√2 1. y" - 4y = 0 4. 16y(4) - 8y"+y=0 √2+√2 √2-1√2 FIGURE 3.20 The four roots of 24 + 16 = 0 lie on a circle of radius 16¹/4 = 2 and have an Eulbus angular separation of 2π/4 = π/2 radians. The roots occur in two complex conjugate pairs. Exercises 1-18: In each exercise, (a) Find the general solution of the differential equation. (b) If initial conditions are specified, solve the initial value problem. Re 2. y"+y" - y - y = 0 5. 16y (4) + 8y"+y = 0 8. y(4)-y=0 7. y" - 2y" - y' + 2y = 0 10. 2y" - y" = 0 11. y" + y = 0 13. y) - y = 0 14. y(4) - y""+y'- y = 0 15. y" + 2y" + y = 0, y(0) = 0, y'(0) = 0, y'(0) = 1 3. y""+y" + 4y + 4y = 0 6. y" - y = 0 9. y"" + 8y = 0 12. y(4) + 2y" + y = 0
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