Find the general solution of the system of equations x' = (² ) x + ( 9 -82 -9 cos t sin t x = Choose one Choose one G₂ (1 CL • sint) + c₂ (² 9 sint + cost sin t st) + ²2 ( 1 ) + cost-1/2 ( 8 ) t sint a(² (9 cost-sint) + c₂ (² 9 sin ( + cost sint ¹) + ( 2 ) t cost-/ ( 8 ) t sint (2) cost-(33) sint 19 cost-sint) + ca (1 (³ 9 sini + cost - sin ost) + 2 ( 2 ) t cost-½ (3) tsint-(2) cost-( 83 ) sint 9 83 9 cost-sint cont ²² ) + ₁₂ (² 9 sint + cost sin t st) - 2 ( 2 ) t cost + (3) tsint-(2) cost-(33) sint ½ 5₂(8 ^²)+ ₁₂ (² 9 sin ( + cost sin t st) - ( 2 ) cost - (83) sint 9 CL 9 cost-sint cont 9 cost-sint cont
Find the general solution of the system of equations x' = (² ) x + ( 9 -82 -9 cos t sin t x = Choose one Choose one G₂ (1 CL • sint) + c₂ (² 9 sint + cost sin t st) + ²2 ( 1 ) + cost-1/2 ( 8 ) t sint a(² (9 cost-sint) + c₂ (² 9 sin ( + cost sint ¹) + ( 2 ) t cost-/ ( 8 ) t sint (2) cost-(33) sint 19 cost-sint) + ca (1 (³ 9 sini + cost - sin ost) + 2 ( 2 ) t cost-½ (3) tsint-(2) cost-( 83 ) sint 9 83 9 cost-sint cont ²² ) + ₁₂ (² 9 sint + cost sin t st) - 2 ( 2 ) t cost + (3) tsint-(2) cost-(33) sint ½ 5₂(8 ^²)+ ₁₂ (² 9 sin ( + cost sin t st) - ( 2 ) cost - (83) sint 9 CL 9 cost-sint cont 9 cost-sint cont
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
![Find the general solution of the system of equations
9
x'
=
- (1 -32)x+ (
cos t
sin t
*).
-9
x = Choose one
Choose one
9
(³
²² ) + c₂ ( st) + 2/(?) t cost-1/2 ( 8 ) t sint
9 sint + cost
sin t
9 sint + cost
9
9
st) + ²2 ( 1 ) t cost-½ (2) tsint - (2)
sin t
0
9 sint + cost
1
ost) + ²2 ( 2 ) t cost - ( 8 ) t sint -
¼
- sint
9 sint + cost
sin t
st) - 2 ( 2 ) t cost + 2 ( 8 ) tsint
9 sint + cost
sin t
C1
2(90
9 cost - sint
cost
9 cost - sint
- cos t
9 cost - sint
cost
a(²
a(²
9 cost - sint
Cost
it).
int).
¹t).
C₂ (8
C1
+ C₂
+ C₂
+ C₂
9 cost-sint
Cost
nt) + c₂ (
83
-1 (8³) s
9
83
( 8³ ) s
9
83
( 33 ) sint
9
cost-
( 2 ) cost -
( 2 ) cost -
cost)-(2) cost-1(83) sint
9
sin t
sin t](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F546ca3ef-5c41-4b6f-8ba8-1af4930ff657%2Ff0c37a76-bdb3-489c-965b-49cc1fd90618%2Fk8oubbf_processed.png&w=3840&q=75)
Transcribed Image Text:Find the general solution of the system of equations
9
x'
=
- (1 -32)x+ (
cos t
sin t
*).
-9
x = Choose one
Choose one
9
(³
²² ) + c₂ ( st) + 2/(?) t cost-1/2 ( 8 ) t sint
9 sint + cost
sin t
9 sint + cost
9
9
st) + ²2 ( 1 ) t cost-½ (2) tsint - (2)
sin t
0
9 sint + cost
1
ost) + ²2 ( 2 ) t cost - ( 8 ) t sint -
¼
- sint
9 sint + cost
sin t
st) - 2 ( 2 ) t cost + 2 ( 8 ) tsint
9 sint + cost
sin t
C1
2(90
9 cost - sint
cost
9 cost - sint
- cos t
9 cost - sint
cost
a(²
a(²
9 cost - sint
Cost
it).
int).
¹t).
C₂ (8
C1
+ C₂
+ C₂
+ C₂
9 cost-sint
Cost
nt) + c₂ (
83
-1 (8³) s
9
83
( 8³ ) s
9
83
( 33 ) sint
9
cost-
( 2 ) cost -
( 2 ) cost -
cost)-(2) cost-1(83) sint
9
sin t
sin t
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