The matrices in the following systems have complex eigenvalues; use Theorem 2 to find the general (real-valued) solution; if initial conditions are given, find the particular solution satisfying them. (a) x' = (c) x' = = 133 3] 4 0 0 X; 0 0 -1 3 -6 x; 5 19 (b) x² = 1 (d) x' = X, 3 x(0) = [ [B] 0 20 -2 0 0 0 3 0 x, ; Sol'n 1 2 3 x(0) »--
The matrices in the following systems have complex eigenvalues; use Theorem 2 to find the general (real-valued) solution; if initial conditions are given, find the particular solution satisfying them. (a) x' = (c) x' = = 133 3] 4 0 0 X; 0 0 -1 3 -6 x; 5 19 (b) x² = 1 (d) x' = X, 3 x(0) = [ [B] 0 20 -2 0 0 0 3 0 x, ; Sol'n 1 2 3 x(0) »--
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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I only need help with problem 2.d. Thank you.
![2. The matrices in the following systems have complex eigenvalues; use Theorem 2
to find the general (real-valued) solution; if initial conditions are given, find the
particular solution satisfying them.
(a) x² = 33
(c) x' =
=
0
0
-1
3
X;
0
-6 x;
5
(b) x'
=
(d) x'
X,
0
2
-2 0
0
0
x(0)
0
0 x,
3
3
=
-[³];
; Sol'n
x(0) =
=
2
3](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F13b8e596-45c0-434d-ab2b-ea5ebc953e71%2Fe24af6ae-6890-41ad-85d0-ee1fe631c688%2Fmgxkdd4_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2. The matrices in the following systems have complex eigenvalues; use Theorem 2
to find the general (real-valued) solution; if initial conditions are given, find the
particular solution satisfying them.
(a) x² = 33
(c) x' =
=
0
0
-1
3
X;
0
-6 x;
5
(b) x'
=
(d) x'
X,
0
2
-2 0
0
0
x(0)
0
0 x,
3
3
=
-[³];
; Sol'n
x(0) =
=
2
3
Transcribed Image Text:following.
Theorem 2. If A is an (nx n)-matrix of real constants that has a complex eigenvalue
X and eigenvector v, then the real and imaginary parts of w(t)
exty are linearly
independent real-valued solutions of (7.17): x₁(t) = Re(w(t)) and x₂(t) = Im(w(t)).
=
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