1550078481-Ordinary_Differential_Equations__Roberts_

Answers to Selected Exercises 549

Exercises 4.2 Roots of Polynomials

1. X1 = 1.36881, X2 = -1.68440 + 3.43133i, X3 = -1.68440 - 3.43133i


2. X1 = .644399, X2 = -1.87214 + 3.81014i, X3 = -1.87214 - 3.81014i,

X4 = 3.09987

7. a. 7.42445 ± 22.7486i, -19. 4245 ± 14.0689i, 24

b. 1, 1.50473 ± .516223i, 1.01797 ± 2.60909i, -6.04539

9. 1 + i, 1 + i, 4 - 3i, 4 + 3i, 3.999 + 3i

Exercises 4.3 Homogeneous Linear Equations with Constant

Coefficients

11. a. y = c1 cos( fox)+ c2 sin( fox)
    17. r^3 - (3 + 4i)r^2 - (4 - 12i)r + 12 = O; 2i, 2i, 3·
    '
    19. We conclude eix = cos x + i sin x for all x E ( -oo, oo).