-3 2 X1 -5 3 X2 d X1 %3D dt X2 cos(t) 3/2cos(t) + 1/2sin(t) sin(t) 3/2sin(t)- 1/2cos(t) + c2 C1 X2 sin(t) 3sin(t) + cos(t) B. X1 cos(t) = C1 3cos(t) – sin(t) + c2 X2 sin(t) 3/2cos(t) +1/2sin(t X1 cos(t) + C2 = C1 [3/2sin(t) – 1/2cos(t) X2 sin(t) 3/2sin(t) +1/2cos(t) D cos(t) 3/2cos(t)- 1/2sin(t) X1 = C1 +C2 %3D X2

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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Solve the following system
-3 2
-5 3 X2
X1
dt X2
sin(t)
cos(t)
3/2cos(t) + 1/2sin(t)|
X1
+ c2
/2sin(t)-1/2cos(t)]
= C1
X2
B
cos(t)
sin(t)
X1
3cos(t) - sin(t) + 3sin(t) + cos(t)
cos(t)
3/2sin(t) – 1/2cos(t)
sin(t)
+ 3/2cos(t) +1/2sin(t)
X1
= C1
X2
sin(t)
3/2sin(t) +1/2cos(t)
cos(t)
- 3/2cos(t) – 1/2sin(t)
X1
+c2
= C1
X2
Transcribed Image Text:Solve the following system -3 2 -5 3 X2 X1 dt X2 sin(t) cos(t) 3/2cos(t) + 1/2sin(t)| X1 + c2 /2sin(t)-1/2cos(t)] = C1 X2 B cos(t) sin(t) X1 3cos(t) - sin(t) + 3sin(t) + cos(t) cos(t) 3/2sin(t) – 1/2cos(t) sin(t) + 3/2cos(t) +1/2sin(t) X1 = C1 X2 sin(t) 3/2sin(t) +1/2cos(t) cos(t) - 3/2cos(t) – 1/2sin(t) X1 +c2 = C1 X2
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