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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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