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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. -3 -12 0 A= 2 -5 4 4 05 Construct the general solution of x' = Ax involving complex eigenfunctions below. #00 H ++ -6 - 31 1 1-2i OA. x(t)=c₁-6 B. X(t)=C₁ OC. X(t)=C₁ OD. X(t) = C₁ 1 0 1+2i 1 3t+C₂ 4+4i-1+it+C3 4-4i-1-t -3t - 6 1-2i HAA 4+4i (1+3i)t + C3 4-4i What is the general real solution? Re(x(t)) = - 6 1+2i (1-3i)t

Construct the general solution of x' =Ax involving complex eigenfunctions and then obtain the general real solution. Describe the shapes of typical trajectories. -3 -12 0 A= 2 -5 4 4 05 Construct the general solution of x' = Ax involving complex eigenfunctions below. #00 H ++ -6 - 31 1 1-2i OA. x(t)=c₁-6 B. X(t)=C₁ OC. X(t)=C₁ OD. X(t) = C₁ 1 0 1+2i 1 3t+C₂ 4+4i-1+it+C3 4-4i-1-t -3t - 6 1-2i HAA 4+4i (1+3i)t + C3 4-4i What is the general real solution? Re(x(t)) = - 6 1+2i (1-3i)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. A = -3 2 4 -12 0 - 5 4 05 Construct the general solution of x' = Ax involving complex eigenfunctions below. OA. X(t) = C₁ B. x(t)=C₁ -2 3t -6 e + C₂ 1 - 3 O C. X(t) = C₁ 3 -2 0 4}} 1 3 0 1-2i 1 -3t+c₂ 4+4i e -2 - 6 Q+ H AA 1-2i (1+3i)t 4+4i e + C3 4-4i e - 6 O D. x(t)=c₁-2 * What is the general real solution? Re(x(t)) = + C₂ 4 3 (−1+i)t e 1+2i + C3 4-4i e - 6 1+2i -6 (-1-i)t (1-3i)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. A = -3 2 4 -12 0 - 5 4 05 Construct the general solution of x' = Ax involving complex eigenfunctions below. OA. X(t) = C₁ B. x(t)=C₁ -2 3t -6 e + C₂ 1 - 3 O C. X(t) = C₁ 3 -2 0 4}} 1 3 0 1-2i 1 -3t+c₂ 4+4i e -2 - 6 Q+ H AA 1-2i (1+3i)t 4+4i e + C3 4-4i e - 6 O D. x(t)=c₁-2 * What is the general real solution? Re(x(t)) = + C₂ 4 3 (−1+i)t e 1+2i + C3 4-4i e - 6 1+2i -6 (-1-i)t (1-3i)t
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