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A = 30 64 23 -11-23 -9 6 15 4 - 3 [ A. X(t)=C₁ B. X(t)=C₁ - c. X(t) = C₁ 23-34 i 1e¹+₂ 9+14 i 3 D. X(t) = C₁ 1 1 1 + C₂ 1e¹+C₂ - 3 9 23 3 What is the general real solution? e(x(t)) = e 2t 23 + 34 i e e (5+2i)t +C3 −9-14 ie (5-2i)t 720-21xX + C3 1 23 + 34 i -3e¹+C₂2-9+14 i e |²g| 1 3 -9 23 - 3 e 23-34 i 23 +34 i −9+14 ie (2-i)t +C3 -9-14 i e(2+i)t 3 3 (5+2i)t - 2t 3 +C3 -9-14 i 23-34 i 3 e (5-2i)t

A = 30 64 23 -11-23 -9 6 15 4 - 3 [ A. X(t)=C₁ B. X(t)=C₁ - c. X(t) = C₁ 23-34 i 1e¹+₂ 9+14 i 3 D. X(t) = C₁ 1 1 1 + C₂ 1e¹+C₂ - 3 9 23 3 What is the general real solution? e(x(t)) = e 2t 23 + 34 i e e (5+2i)t +C3 −9-14 ie (5-2i)t 720-21xX + C3 1 23 + 34 i -3e¹+C₂2-9+14 i e |²g| 1 3 -9 23 - 3 e 23-34 i 23 +34 i −9+14 ie (2-i)t +C3 -9-14 i e(2+i)t 3 3 (5+2i)t - 2t 3 +C3 -9-14 i 23-34 i 3 e (5-2i)t

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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Construct the general solution of x' = Ax involving complex eigenfunctions and then obtain the general real solution. Describe the shapes of typical trajectories. 30 64 23 -11 -23 -9 6 15 4 A = A. X(t) = C₁ OB. X(t) = C₁ OC. X(t) = C₁ - 3 1 1 1 1 1 O D. X(t) = C₁ -3 23 - 34 i -C₂-9+14 i 3 -t (5+2i)t -9 2t 23 e2+ C3 3 23 + 34 i -C₂-9+14 i 3 What is the general real solution? Re(x(t)) = 23 + 34 i +C3-9-14 i 3 23 - 34 i -9+14 ie (²-)t + C3 3 -9 23 - 3 - 2t (5+2i)t + C3) 23 + 34 i -9-14 ie (2+i)t 3 -9-14 i 23 - 34 i e 3 (5-2i)t e (5-2i)t
Transcribed Image Text:Construct the general solution of x' = Ax involving complex eigenfunctions and then obtain the general real solution. Describe the shapes of typical trajectories. 30 64 23 -11 -23 -9 6 15 4 A = A. X(t) = C₁ OB. X(t) = C₁ OC. X(t) = C₁ - 3 1 1 1 1 1 O D. X(t) = C₁ -3 23 - 34 i -C₂-9+14 i 3 -t (5+2i)t -9 2t 23 e2+ C3 3 23 + 34 i -C₂-9+14 i 3 What is the general real solution? Re(x(t)) = 23 + 34 i +C3-9-14 i 3 23 - 34 i -9+14 ie (²-)t + C3 3 -9 23 - 3 - 2t (5+2i)t + C3) 23 + 34 i -9-14 ie (2+i)t 3 -9-14 i 23 - 34 i e 3 (5-2i)t e (5-2i)t
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