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17. y" + 3y" + 3y + y = 0, y(0) = 0, y'(0) = 1, y" (0) = 0

17. y" + 3y" + 3y + y = 0, y(0) = 0, y'(0) = 1, y" (0) = 0

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 17.
stank Second and Higher Order Linear Differential Equations 16. y" + 4y = 0, y(0) = 1, y'(0) = 6, y" (0) = 4 17. y"" + 3y" + 3y' + y = 0, y(0) = 0, y'(0) = 1, y" (0) = 0 18. y(4) -y = 0, y(0) = 0, y'(0) = 0, y" (0) = 0, y" (0) = 1 Exercises 19-20: The given differential equations have repeated roots; a and ß are re (5) (6) of appropriate, to determine a solutior
Transcribed Image Text:stank Second and Higher Order Linear Differential Equations 16. y" + 4y = 0, y(0) = 1, y'(0) = 6, y" (0) = 4 17. y"" + 3y" + 3y' + y = 0, y(0) = 0, y'(0) = 1, y" (0) = 0 18. y(4) -y = 0, y(0) = 0, y'(0) = 0, y" (0) = 0, y" (0) = 1 Exercises 19-20: The given differential equations have repeated roots; a and ß are re (5) (6) of appropriate, to determine a solutior
y(t) = evit (c₁ cos √2t+c₂ sin √2t) + e-√21 (c3 cos √2t+c4 sin When a is a real number, the complex roots of ". -A= 0 occur conjugate pairs. If we plot these n roots in the complex plane, we lie on a circle of radius la¹/n and the angular separation between ro Figure 3.20 shows the four roots of λ + 16 = 0 found in Example -√2+i√2, -√2-√2 Im √2 + √2 √2-√2 Re FIGURE 3.20 The four roots of 24 + 16 = 0 lie on a circle of radius 16¹/4 = 2 and orangular separation of 2π/4 = π/2 radians. The roots occur in two 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.
Transcribed Image Text:y(t) = evit (c₁ cos √2t+c₂ sin √2t) + e-√21 (c3 cos √2t+c4 sin When a is a real number, the complex roots of ". -A= 0 occur conjugate pairs. If we plot these n roots in the complex plane, we lie on a circle of radius la¹/n and the angular separation between ro Figure 3.20 shows the four roots of λ + 16 = 0 found in Example -√2+i√2, -√2-√2 Im √2 + √2 √2-√2 Re FIGURE 3.20 The four roots of 24 + 16 = 0 lie on a circle of radius 16¹/4 = 2 and orangular separation of 2π/4 = π/2 radians. The roots occur in two 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.
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