Construct the general solution of x' = Ax involving complex eigenfunctions and then obtain the general real solution. Describe the shapes of typical trajectories. 5 -2 A= 10 Choose the correct general solution of x' = Ax involving complex eigenfunctions below. -2 O A. C1 10 - 3 -2 5t - 3t O B. C1 2- (1-2i)t О с. С1 5+ -2 (1+21)t 10 2 iyt OD. C1 -3-i Choose the correct general real solution below. 2 cos (21) - sin (21) 2 sin (2t) + cos (2t) A. C4 5 cos (21) 5 sin (21) 2 cos (21) 2 i sin (21) + i cos (21) - sin (21) В. С, 5 cos (21) - 5i sin (21) -2 С. С1 10 -3 -2 5t+ -3t D. C1 The trajectories 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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For the final part of the question choose between the three options on whether:

 

The trajectories 

a) spiral outward from

b) spiral inward toward 

c) form ellipses around

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.
5 -2
A =
10 -3
Choose the correct general solution of x' = Ax involving complex eigenfunctions below.
-2
A. C4
10
-3
-2
5t
e
- 3t
e
В. С,
2+
2-
(1-21)t
Oc. C4
5+
-2
(1-2it
O D. C1
10
-3-i
Choose the correct general real solution below.
2 cos (21) - sin (2t)
2 sin (2t) + cos (2t)
A. C
5 cos (2t)
5 sin (21)
2 cos (21)
2i sin (21) + i cos (21) - sin (21)
В. С1
5 cos (2t)
- 5i sin (2t)
-2
-t
le
Oc. C4
10
-3
2
5t
D. C1
-2
- 3t
The trajectories
the origin.
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. 5 -2 A = 10 -3 Choose the correct general solution of x' = Ax involving complex eigenfunctions below. -2 A. C4 10 -3 -2 5t e - 3t e В. С, 2+ 2- (1-21)t Oc. C4 5+ -2 (1-2it O D. C1 10 -3-i Choose the correct general real solution below. 2 cos (21) - sin (2t) 2 sin (2t) + cos (2t) A. C 5 cos (2t) 5 sin (21) 2 cos (21) 2i sin (21) + i cos (21) - sin (21) В. С1 5 cos (2t) - 5i sin (2t) -2 -t le Oc. C4 10 -3 2 5t D. C1 -2 - 3t The trajectories the origin.
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