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Consider a system of two linear first-order ordinary differential equations: Y₁ = Y1 — Y2, _Y2 = 2y1 - y2 . a) The corresponding A₁ = 1, A₂ = -1 b) The corresponding OIII and IV where I:U₁ = II:4₂ = III:₁ eigenvalues are 1+ 2 1-i (¹+¹) (¹3²) (2(2²+4)) (2(1²+-1)) i) IV:u₂ = OA₁ = 1 + 1, A₂ = 1 - i OA₁i, A₂ i = eigenvectors of this linear ODE system are: OII and III OI and IV = OI and II c) The phase portrait for this system of ODEs is Stable focus with spiral in Centre Unstable focus with spiral out Stable node

Consider a system of two linear first-order ordinary differential equations: Y₁ = Y1 — Y2, _Y2 = 2y1 - y2 . a) The corresponding A₁ = 1, A₂ = -1 b) The corresponding OIII and IV where I:U₁ = II:4₂ = III:₁ eigenvalues are 1+ 2 1-i (¹+¹) (¹3²) (2(2²+4)) (2(1²+-1)) i) IV:u₂ = OA₁ = 1 + 1, A₂ = 1 - i OA₁i, A₂ i = eigenvectors of this linear ODE system are: OII and III OI and IV = OI and II c) The phase portrait for this system of ODEs is Stable focus with spiral in Centre Unstable focus with spiral out Stable node

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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Consider a system of two linear first-order ordinary differential equations: y₁ = y₁ - y2, y₂ = 2y1 - y2 - a) The corresponding Oλ₁ = 1, №₂ = −1 b) The corresponding OIII and IV where 1:4₁ = II:42 = 1+ 2 (¹+4) (¹3²) 1 - 2i 2(1 + i) (2(1²-+-+)) i) III:u1 IV:4₂ = eigenvalues are = OA₁ = 1 + 1, A₂ = 1 - i OA₁i, A₂ = −i = eigenvectors of this linear ODE system are: Oll and III OI and IV OI and II c) The phase portrait for this system of ODEs is Stable focus with spiral in Centre Unstable focus with spiral out Stable node
Transcribed Image Text:Consider a system of two linear first-order ordinary differential equations: y₁ = y₁ - y2, y₂ = 2y1 - y2 - a) The corresponding Oλ₁ = 1, №₂ = −1 b) The corresponding OIII and IV where 1:4₁ = II:42 = 1+ 2 (¹+4) (¹3²) 1 - 2i 2(1 + i) (2(1²-+-+)) i) III:u1 IV:4₂ = eigenvalues are = OA₁ = 1 + 1, A₂ = 1 - i OA₁i, A₂ = −i = eigenvectors of this linear ODE system are: Oll and III OI and IV OI and II c) The phase portrait for this system of ODEs is Stable focus with spiral in Centre Unstable focus with spiral out Stable node
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