3. Find the general solution of the system of differential equations * - ()* d 8 -5 10 + 4°c ( cos(7t) – 7 sin(7t) ) .o7 7. 10 cos(7t) 7 cos(7t) + sin(7t) ). 10 sin(7t) + 8t"e7 (
3. Find the general solution of the system of differential equations * - ()* d 8 -5 10 + 4°c ( cos(7t) – 7 sin(7t) ) .o7 7. 10 cos(7t) 7 cos(7t) + sin(7t) ). 10 sin(7t) + 8t"e7 (
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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Question
Linear Methods
![3. Find the general solution of the system of differential equations
d
8 -5
X =
dt
10
+ 4t°,7t ( cos(7t) – 7 sin(7t)
10 cos(7t)
7 cos(7t) + sin(7t)
10 sin(7t)
).
-
+ 8t°et
Hint: The characteristic polynomial of the coefficient matrix is X² – 14) +98. Moreover
X,(t) = t*et ( cos(7t) – 7 sin(7t) )
10 cos(7t)
7 cos(7t) + sin(7t)
10 sin(7t)
+ t°e7t
is a particular solution of the system.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe525a968-d29b-48fb-a7c8-70d47cdcaf9d%2F5b072273-9ed2-4bd1-b38c-abab2a5b03cd%2F8idbn2k_processed.png&w=3840&q=75)
Transcribed Image Text:3. Find the general solution of the system of differential equations
d
8 -5
X =
dt
10
+ 4t°,7t ( cos(7t) – 7 sin(7t)
10 cos(7t)
7 cos(7t) + sin(7t)
10 sin(7t)
).
-
+ 8t°et
Hint: The characteristic polynomial of the coefficient matrix is X² – 14) +98. Moreover
X,(t) = t*et ( cos(7t) – 7 sin(7t) )
10 cos(7t)
7 cos(7t) + sin(7t)
10 sin(7t)
+ t°e7t
is a particular solution of the system.
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