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Verify that the vector Xp is a particular solution of the given nonhomogeneous linear system. dx dt dy - (-₁) ₁ + (₁) t dt Writing the system in the form X' = AX + F for some coefficient matrix A and vector F, one obtains the following. X'= For Xp 1 3 = x + 4y + 2t - 9 = 3x + 2y — 4t - 24; X = 4 X₂' 2 = ·(-²) ₁ + (1). 2 2 X + t one has 2 -4 + -9 -24

Verify that the vector Xp is a particular solution of the given nonhomogeneous linear system. dx dt dy - (-₁) ₁ + (₁) t dt Writing the system in the form X' = AX + F for some coefficient matrix A and vector F, one obtains the following. X'= For Xp 1 3 = x + 4y + 2t - 9 = 3x + 2y — 4t - 24; X = 4 X₂' 2 = ·(-²) ₁ + (1). 2 2 X + t one has 2 -4 + -9 -24

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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Verify that the vector Xp is a particular solution of the given nonhomogeneous linear system. dx dt dy L = 3x + 2y − 4t - 24; X₁ = (-²)t + -(-³)₁ + (²) dt Writing the system in the form X' = AX + F for some coefficient matrix A and vector F, one obtains the following. X'= For Xp 1 3 = x + 4y + 2t - 9 AXp 2 9×8·3 X + t -4 X₂' = = (-²)² + (²) 4 + F = 2 2 2 one has -1 Since the above expressions are equal + -9 -24 ~~~ ·x₂ - (-²) ₁ + (²) = is a particular solution of the given system.
Transcribed Image Text:Verify that the vector Xp is a particular solution of the given nonhomogeneous linear system. dx dt dy L = 3x + 2y − 4t - 24; X₁ = (-²)t + -(-³)₁ + (²) dt Writing the system in the form X' = AX + F for some coefficient matrix A and vector F, one obtains the following. X'= For Xp 1 3 = x + 4y + 2t - 9 AXp 2 9×8·3 X + t -4 X₂' = = (-²)² + (²) 4 + F = 2 2 2 one has -1 Since the above expressions are equal + -9 -24 ~~~ ·x₂ - (-²) ₁ + (²) = is a particular solution of the given system.
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