8. y(4)-y=0
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.4: Complex And Rational Zeros Of Polynomials
Problem 14E
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Transcribed Image Text:S
-√2+i√2
-√2-√2
√2+ i√2
√2-1√2
1. y" - 4y = 0
4. 16y) - 8y" + y = 0
7. y" - 2y" - y' + 2y = 0
FIGURE 3.20
The four roots of 24+ 16 = 0 lie on a circle of radius 16¹/4 = 2 and have an
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
10. 2y"" - y" = 0
11. y" + y = 0
13. y) - y = 0
14. y
- 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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