Construct the general solution of x' = Ax involving complex eigenfunctions and then obtain the general real solution. Describe the shapes of typical trajectories. A = 4:1 6 12 5 15 6 Choose the correct general solution of x' = Ax involving complex eigenfunctions below. +02 ○ A. x(t) = c₁ 12 15 PHP -- - 9t 9t 1 + i 1-i (9+3i)t (9. -3i)t B. x(t) = c₁ +02 5 5 6 12+ i - (9+3i)t ○ c. x(t) = c₁ +02 5 e(9 – 3i)t 15 6-i 1 5 * * ○ D. x(t) = c₁ 5 12t + C21 6t +02 What is the general real solution? Re(x(t)) = Describe the shapes of typical trajectories of Re(x(t)). Choose the correct answer below. The trajectories spiral inward toward from the origin. The trajectories form ellipses around the origin. The trajectories spiral outward from the origin.
Construct the general solution of x' = Ax involving complex eigenfunctions and then obtain the general real solution. Describe the shapes of typical trajectories. A = 4:1 6 12 5 15 6 Choose the correct general solution of x' = Ax involving complex eigenfunctions below. +02 ○ A. x(t) = c₁ 12 15 PHP -- - 9t 9t 1 + i 1-i (9+3i)t (9. -3i)t B. x(t) = c₁ +02 5 5 6 12+ i - (9+3i)t ○ c. x(t) = c₁ +02 5 e(9 – 3i)t 15 6-i 1 5 * * ○ D. x(t) = c₁ 5 12t + C21 6t +02 What is the general real solution? Re(x(t)) = Describe the shapes of typical trajectories of Re(x(t)). Choose the correct answer below. The trajectories spiral inward toward from the origin. The trajectories form ellipses around the origin. The trajectories spiral outward from the origin.
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 =
4:1
6
12
5
15
6
Choose the correct general solution of x' = Ax involving complex eigenfunctions below.
+02
○ A. x(t) = c₁
12
15
PHP
--
- 9t
9t
1 + i
1-i
(9+3i)t
(9.
-3i)t
B. x(t) = c₁
+02
5
5
6
12+ i
-
(9+3i)t
○ c. x(t) = c₁
+02
5
e(9 – 3i)t
15
6-i
1
5
* *
○ D. x(t) = c₁
5
12t + C21
6t
+02
What is the general real solution?
Re(x(t)) =
Describe the shapes of typical trajectories of Re(x(t)). Choose the correct answer below.
The trajectories spiral inward toward from the origin.
The trajectories form ellipses around the origin.
The trajectories spiral outward from the origin.
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