(2 cos 2t /19. Assume that a real 2 x 2 matrix A has an eigenvalue of A1 = 3+ 2i with a correspondingeigenvector = (6)Find the general solution of the system of differential equations2igiven by글 %=D Az.cos 2tsin 2t교(t) = cie3t( sin 2t+ cze³t2 cos 2tcos 2tsin 2ta(t) = c1e3t+ cze3t-2 sin 2t2 cos 2t(.cos 2tsin 2ta(t)Ciešt+ cze3tsin 2t- cos 2t(-2 cos 2tsin 2ta(t) = cie3t+ cze3tsin 2t-2 cos 2tcos 2t( 2 sin 2t)sin 2ta(t) = c1e3t+ cze³t2 cos 2t

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Answered: Assume that a real 2 x 2 matrix A has…

Assume that a real 2 x 2 matrix A has an eigenvalue of 1 = 3 + 2i with a corresponding eigenvector = (C) Find the general solution of the system of differential equations 2i given by i' = Aã.

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

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

(2 cos 2t /
19. Assume that a real 2 x 2 matrix A has an eigenvalue of A1 = 3+ 2i with a corresponding
eigenvector = (6)
Find the general solution of the system of differential equations
2i
given by
글 %=D Az.
cos 2t
sin 2t
교(t) = cie3t
( sin 2t
+ cze³t
2 cos 2t
cos 2t
sin 2t
a(t) = c1e3t
+ cze3t
-2 sin 2t
2 cos 2t
(.
cos 2t
sin 2t
a(t)
Ciešt
+ cze3t
sin 2t
- cos 2t
(
-2 cos 2t
sin 2t
a(t) = cie3t
+ cze3t
sin 2t
-2 cos 2t
cos 2t
( 2 sin 2t
)
sin 2t
a(t) = c1e3t
+ cze³t
2 cos 2t

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