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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. x' = -22-26-2 18 22 -18-18 2 2 x; X₁ = e-4t 4 3 3 x₂ = e2t| The vector x₁ is a solution of the given system because x₁' and x3 = e4t| 0 -22-26-2 18 22 - 18 - 18 2 x₁ are both equal to 2

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. x' = -22-26-2 18 22 -18-18 2 2 x; X₁ = e-4t 4 3 3 x₂ = e2t| The vector x₁ is a solution of the given system because x₁' and x3 = e4t| 0 -22-26-2 18 22 - 18 - 18 2 x₁ are both equal to 2

Advanced Engineering Mathematics
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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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. x' = 4 2 x; x₁ = e-4-3, x₂ = e²t| - 22 - 26 -2 18 22 - 18 - 18 2 3 1 -1, X3=e4t 1 The vector x₁ is a solution of the given system because x₁' and 1 - 1 0 - 22 - 26 18 22 - 18 - 18 - 2 2 x₁ are both equal to 2
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. x' = 4 2 x; x₁ = e-4-3, x₂ = e²t| - 22 - 26 -2 18 22 - 18 - 18 2 3 1 -1, X3=e4t 1 The vector x₁ is a solution of the given system because x₁' and 1 - 1 0 - 22 - 26 18 22 - 18 - 18 - 2 2 x₁ are both equal to 2
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