For the final part of the question choose between the three options on whether: The trajectories a) spiral outward fromb) spiral inward toward c) form ellipses aroundthe 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 -2A =10 -3Choose the correct general solution of x' = Ax involving complex eigenfunctions below.-2A. C410-3-25te- 3teВ. С,2+2-(1-21)tOc. C45+-2(1-2itO D. C110-3-iChoose the correct general real solution below.2 cos (21) - sin (2t)2 sin (2t) + cos (2t)A. C5 cos (2t)5 sin (21)2 cos (21)2i sin (21) + i cos (21) - sin (21)В. С15 cos (2t)- 5i sin (2t)-2-tleOc. C410-325tD. C1-2- 3tThe trajectoriesthe origin.

Answered: Image /qna-images/answer/41fd30d0-3175-44b4-9291-d706a9ca84cb.jpg

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.

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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Concept explainers

Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.

Question

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.

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