First verify that the given vectors are solutions of the given system. Then use the Wronskian to show that they are linearly independent. Finally, write the general solution of the system. -4 4 e 4t e -7t x' = x; X1 = ,X2 = 4 e 20 - 12 5e 4t - 7t 9 - 4 - 4 4t 4 e 16 e 4t X1 20 - 12 = x,' 20 - 12 5e 4t 20 e 4t 9 - 4 9. - 4 - 7t -7e -7t X2 20 - 12 = X2' - 7t 20 - 12 4 e – 7t - 28 e The Wronskian of the solutions is W= 11 e -3t II II
First verify that the given vectors are solutions of the given system. Then use the Wronskian to show that they are linearly independent. Finally, write the general solution of the system. -4 4 e 4t e -7t x' = x; X1 = ,X2 = 4 e 20 - 12 5e 4t - 7t 9 - 4 - 4 4t 4 e 16 e 4t X1 20 - 12 = x,' 20 - 12 5e 4t 20 e 4t 9 - 4 9. - 4 - 7t -7e -7t X2 20 - 12 = X2' - 7t 20 - 12 4 e – 7t - 28 e The Wronskian of the solutions is W= 11 e -3t II II
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:First verify that the given vectors are solutions of the given system. Then use the Wronskian to show that
they are linearly independent. Finally, write the general solution of the system.
- 4
x; X1 =
4e 4t
- 7t
X':
20 - 12
X2
4t
5 e
4 e
- 7t
9.
-4
4t
4 e
4t
16 e
X1
20 - 12
= x,'
20 - 12
5 e 4t
20 e 4t
9
- 4
- 4
- 7t
-7e -7t
e
X2
20 - 12
- 7t
4 e
=x2"
- 7t
20 - 12
- 28 e
The Wronskian of the solutions is W = 11 e - 3t.
II
4.
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