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

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Description: I'm just confused on how to calculate the Wronskian... First verify that the given vectors are solutions of the given system. Then use the Wronskian to show thatthey are linearly independent. Finally, write the general solution of the system.- 4x; X1

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

I'm just confused on how to calculate the Wronskian...

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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