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Consider a system of two linear first-order ordinary differential equations: y₁ = y₁ - y2, y2 = 2y1 - y2 a) The corresponding eigenvalues are OA₁i, A₂ = -i OA₁ = 1+i, A₂ = 1-i O₁ = 1, A₂ = -1 = b) The corresponding eigenvectors of this linear ODE system are: Oll and III OI and IV OIII and IV OI and II where I:U₁ = II:u₂ = III:u₁ = IV:42 out 1+ 1 + i 2 (¹-1) 3 2i ( 2 ( 1² + i)) (2(1²+ 4)) i) c) The phase portrait for this system of ODEs is OUnstable focus with spiral Stable node Ostable focus with Centre spiral in

Consider a system of two linear first-order ordinary differential equations: y₁ = y₁ - y2, y2 = 2y1 - y2 a) The corresponding eigenvalues are OA₁i, A₂ = -i OA₁ = 1+i, A₂ = 1-i O₁ = 1, A₂ = -1 = b) The corresponding eigenvectors of this linear ODE system are: Oll and III OI and IV OIII and IV OI and II where I:U₁ = II:u₂ = III:u₁ = IV:42 out 1+ 1 + i 2 (¹-1) 3 2i ( 2 ( 1² + i)) (2(1²+ 4)) i) c) The phase portrait for this system of ODEs is OUnstable focus with spiral Stable node Ostable focus with Centre spiral in

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: y₁y₁ - y2, y2 = 2y1 - y2 . a) The corresponding eigenvalues are OA₁ = 1, A₂ i O₁ = 1+ i, A₂ I:U₁ b) The corresponding eigenvectors of this linear ODE system are: Oll and III OIII and IV OI and II OI and IV where = II:42 III:u₁ IV:42 out = (¹7²) 2 1- i 3 2i (2(12²+ i)) ( 2 (1 ²+ i) 2 = = = - 1-i OA₁1, A₂ = -1 c) The phase portrait for this system of ODEs is OUnstable focus with spiral Stable node Stable focus with Centre spiral in
Transcribed Image Text:Consider a system of two linear first-order ordinary differential equations: y₁y₁ - y2, y2 = 2y1 - y2 . a) The corresponding eigenvalues are OA₁ = 1, A₂ i O₁ = 1+ i, A₂ I:U₁ b) The corresponding eigenvectors of this linear ODE system are: Oll and III OIII and IV OI and II OI and IV where = II:42 III:u₁ IV:42 out = (¹7²) 2 1- i 3 2i (2(12²+ i)) ( 2 (1 ²+ i) 2 = = = - 1-i OA₁1, A₂ = -1 c) The phase portrait for this system of ODEs is OUnstable focus with spiral Stable node Stable focus with Centre spiral in
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