Find the general solution of the given system of equations. X = C1 X = C₁ X = C1 X = C1 X = C₁ 9 cost - sint cost 9 cost - sint - cost 9 cost - sint cost 9 cost - sint cost 9 cost - sint - cost + C₂ + C₂ + C₂ + C₂ + C₂ 9-82 cost x' x = (₁ - $2²) x + (-COST) 1 -9 sint 9 sint + cost sint 9 sint - cost - sint 1 83 ) - 17 (2) cost - 7 (8³) 4 9 9 ³) - /²2 (²) ₁ 9 ) + ²/(?) 9 sint + cost sint 9 sint + cost sint 9 sint - cost - sint 1 9 - (2) 2 t cost + t cost - sint 9 () + ²/(?) 1 cost - 1/2 (3) t 2 t sint 1 t sint 4 (2) c 1 9 1 1 - (3) sint-(2) cost - t 2 4 cost - 83 -1 (8³), t 4 9 9 1 1 1 ¹)-2²2 (2) 1 cost+ (3) sint - (2) cost - t t 4 4 (83) sinf 9 (83) sint 9
Find the general solution of the given system of equations. X = C1 X = C₁ X = C1 X = C1 X = C₁ 9 cost - sint cost 9 cost - sint - cost 9 cost - sint cost 9 cost - sint cost 9 cost - sint - cost + C₂ + C₂ + C₂ + C₂ + C₂ 9-82 cost x' x = (₁ - $2²) x + (-COST) 1 -9 sint 9 sint + cost sint 9 sint - cost - sint 1 83 ) - 17 (2) cost - 7 (8³) 4 9 9 ³) - /²2 (²) ₁ 9 ) + ²/(?) 9 sint + cost sint 9 sint + cost sint 9 sint - cost - sint 1 9 - (2) 2 t cost + t cost - sint 9 () + ²/(?) 1 cost - 1/2 (3) t 2 t sint 1 t sint 4 (2) c 1 9 1 1 - (3) sint-(2) cost - t 2 4 cost - 83 -1 (8³), t 4 9 9 1 1 1 ¹)-2²2 (2) 1 cost+ (3) sint - (2) cost - t t 4 4 (83) sinf 9 (83) sint 9
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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Transcribed Image Text:Find the general solution of the given system of equations.
x = (i
X = C1
X = C1
X = C1
X = C1
X = C1
9 cost - sint
cost
9 cost - sint
- cost
9 cost - sint
cost
9 cost sint
cost
9 cost - sint
(²
- cost
+ C₂
+ C₂
+ C2
+ C₂
+ C₂
) -
9 sint + cost
sint
=)x + (-5)
-9
9 sint cost
- sint
9 sint + cost
sint
9 sint + cost
sint
9 sint - cost
- sint
9 82
1
(2)
1+ (2) cost - - (83) sint
4
4
9
1
') (²)
- ²1 (2) + const + 1 (2) + sine -
t
t
2
2
0
4
9
¹) + ²/² ( ²9 )
2
t cost
9
t cost
) + 2/2 (²)
1)-(2) cost+
(²)
9
t
-
1
1
(3) + sin -
t
9
(3) sine
2
1
4
(2) -
cost
(2) cost -
83
t
(₂) ¹
(8³)
(83) sin
9
1
4
1
9
1
1
83
¹1 ₁
(3) sin(2) cost-(33) sint
t
4
4 9
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