A₁ = 5 + 2i with ₁ and A₂ = 5 - 2i with 7₂ Write the general real solution for the linear system 7' = A7, in the following forms: x(t) y(t) = A. In eigenvalue/eigenvector form: = [0]. + C₂ 1 -2i 1 B. In fundamental matrix form: 2 1 2 e^(5t)cos(2t) 2e^(5t)sin(2t) cos(2t) cos(2t) C. As two equations: (write "c1" and "c2" for C₁ and ₂) x(t) = c1e^(5t)cos(2t)+c2e^(5t)sin(2t) y(t) = c1*2e^(5t)sin(2t)-c2*2e^(5t)cos(2t) + 0 2 e^(5t)sin(2t) -2e^(5t)cos(21) 2 sin(2t) sin(2t) [a] e 5 e 5 t
A₁ = 5 + 2i with ₁ and A₂ = 5 - 2i with 7₂ Write the general real solution for the linear system 7' = A7, in the following forms: x(t) y(t) = A. In eigenvalue/eigenvector form: = [0]. + C₂ 1 -2i 1 B. In fundamental matrix form: 2 1 2 e^(5t)cos(2t) 2e^(5t)sin(2t) cos(2t) cos(2t) C. As two equations: (write "c1" and "c2" for C₁ and ₂) x(t) = c1e^(5t)cos(2t)+c2e^(5t)sin(2t) y(t) = c1*2e^(5t)sin(2t)-c2*2e^(5t)cos(2t) + 0 2 e^(5t)sin(2t) -2e^(5t)cos(21) 2 sin(2t) sin(2t) [a] e 5 e 5 t
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![A₁ = 5 + 2i with ₁
and
2 = 5-24 with ₂ = [21]
Write the general real solution for the linear system'
=
A. In eigenvalue/eigenvector form:
[20] ([
x(t)
[2]
-2i
=
=
+ C₂
B. In fundamental matrix form:
1
2
2
e^(5t)cos(2t)
2e^(5t)sin(2t)
cos(2t)
=
C. As two equations: (write "c1" and "c2" for C₁ and C₂)
x(t)
c1e^(5t)cos(2t)+c2e^(5t)sin(2t)
y(t) = c1*2e^(5t)sin(2t)-c2*2e^(5t)cos(2t)
cos(2t)
AT, in the following forms:
+
0
2
19
2
e^(5t)sin(2t)
-2e^(5t)cos(2t)
sin(2t)
sin(2t)
Note: if you are feeling adventurous you could use other eigenvectors like 47₁ or -37₂.
e
5
e
01
5
t](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F24d2d084-e1b8-4965-aed3-95c7dd8fa933%2Faf76b4fc-a660-4722-9cc8-4eada6ab398d%2F36l86dc_processed.png&w=3840&q=75)
Transcribed Image Text:A₁ = 5 + 2i with ₁
and
2 = 5-24 with ₂ = [21]
Write the general real solution for the linear system'
=
A. In eigenvalue/eigenvector form:
[20] ([
x(t)
[2]
-2i
=
=
+ C₂
B. In fundamental matrix form:
1
2
2
e^(5t)cos(2t)
2e^(5t)sin(2t)
cos(2t)
=
C. As two equations: (write "c1" and "c2" for C₁ and C₂)
x(t)
c1e^(5t)cos(2t)+c2e^(5t)sin(2t)
y(t) = c1*2e^(5t)sin(2t)-c2*2e^(5t)cos(2t)
cos(2t)
AT, in the following forms:
+
0
2
19
2
e^(5t)sin(2t)
-2e^(5t)cos(2t)
sin(2t)
sin(2t)
Note: if you are feeling adventurous you could use other eigenvectors like 47₁ or -37₂.
e
5
e
01
5
t
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