I am struggling to find the solution for the system x(t) and y(t), given the information highlighted in green. Can you please explain the steps to better understand?
I am struggling to find the solution for the system x(t) and y(t), given the information highlighted in green. Can you please explain the steps to better understand?
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 am struggling to find the solution for the system x(t) and y(t), given the information highlighted in green. Can you please explain the steps to better understand?
![x² = 213 x + 1269.
y₁ = 360x213 y
fx
[
A
213 126
-360 -213
det (A-1) = 0
(A-21) =
det (A-2)
ChA (2):
eigenvaluer of A =
=
t
} []
[₂
f
x(0) = -14
y 10) = 24
213-7 126
360 -213-2J
213-77126
-360 -213-7.
[7]
(2(3-7) (-213-7) + 45360
-45369-2137+21371 +2² +45360
72 +9
Ch 4 (a)=0
7²+9=0
(7+3(7-3)=0
7=-3,3](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9d5b5049-d8dd-402a-aa3b-0cfd97dc82be%2Ffed128ea-bb5f-4e30-b745-f4c64997816a%2F3c8luvm_processed.png&w=3840&q=75)
Transcribed Image Text:x² = 213 x + 1269.
y₁ = 360x213 y
fx
[
A
213 126
-360 -213
det (A-1) = 0
(A-21) =
det (A-2)
ChA (2):
eigenvaluer of A =
=
t
} []
[₂
f
x(0) = -14
y 10) = 24
213-7 126
360 -213-2J
213-77126
-360 -213-7.
[7]
(2(3-7) (-213-7) + 45360
-45369-2137+21371 +2² +45360
72 +9
Ch 4 (a)=0
7²+9=0
(7+3(7-3)=0
7=-3,3
![x(+)
(+26
3
eigenialne
Ge-3t
eigenvector
Solution to System Cr.
[+]
-12
x(+) = 7 (₁ e-³t = 3 G₂ e 3t
+
x+x= 7 (-66₂) ²³²
e3t
eigen eigenvector
3+
3
पु
+ Ge
3t
уг+)
y2+) = -√2 (₁ e-³2 -5 (₂ e
12
X(0) = 7C₁0-³3 + 36₂²₂e²+ = -√4
74
76₁ + 36₂ = -14
C₂ = - 1 (₁+2) = 1 ( 66 +2) =
448
3
y (0) = -12 C₁ e-37-5 C₂ e ²³+ = 24
-12 C₁ - 5 (- 1²)√(²₁+2) = 24
3
G
+3 (417) e
е
=-66
3t
-37
= -462 e
+448 езд
-37
yet) = -12(+1²46) e ²² -15 (2²8) @ ²+ = -792 0²³²-2240
e
34
e](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9d5b5049-d8dd-402a-aa3b-0cfd97dc82be%2Ffed128ea-bb5f-4e30-b745-f4c64997816a%2Fchrrs3n_processed.png&w=3840&q=75)
Transcribed Image Text:x(+)
(+26
3
eigenialne
Ge-3t
eigenvector
Solution to System Cr.
[+]
-12
x(+) = 7 (₁ e-³t = 3 G₂ e 3t
+
x+x= 7 (-66₂) ²³²
e3t
eigen eigenvector
3+
3
पु
+ Ge
3t
уг+)
y2+) = -√2 (₁ e-³2 -5 (₂ e
12
X(0) = 7C₁0-³3 + 36₂²₂e²+ = -√4
74
76₁ + 36₂ = -14
C₂ = - 1 (₁+2) = 1 ( 66 +2) =
448
3
y (0) = -12 C₁ e-37-5 C₂ e ²³+ = 24
-12 C₁ - 5 (- 1²)√(²₁+2) = 24
3
G
+3 (417) e
е
=-66
3t
-37
= -462 e
+448 езд
-37
yet) = -12(+1²46) e ²² -15 (2²8) @ ²+ = -792 0²³²-2240
e
34
e
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