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Consider a system of two linear first-order ordinary differential equations: y₁ = y₁ - y2, y₂ a) The corresponding eigenvalues are Oλ₁ = 1, λ₂ = −1 b) The corresponding eigenvectors of this linear ODE system are: OI and IV Oll and III OIII and IV where I:u₁ II:u₂ = III:u₁ = = 1+i 2 (¹5¹) 3 2i 2(1 + i) • (20₁²+1) 2(1 + i) IV:u₂ = Oλ₁ = i, λ₂ = −i c) The phase portrait for this system of ODEs is Centre OUnstable focus with spiral out Oλ₁ = 1 + i, λ₂ = 1 - i Stable node OI and II = 2y1 - y2. OStable focus with spiral in

Consider a system of two linear first-order ordinary differential equations: y₁ = y₁ - y2, y₂ a) The corresponding eigenvalues are Oλ₁ = 1, λ₂ = −1 b) The corresponding eigenvectors of this linear ODE system are: OI and IV Oll and III OIII and IV where I:u₁ II:u₂ = III:u₁ = = 1+i 2 (¹5¹) 3 2i 2(1 + i) • (20₁²+1) 2(1 + i) IV:u₂ = Oλ₁ = i, λ₂ = −i c) The phase portrait for this system of ODEs is Centre OUnstable focus with spiral out Oλ₁ = 1 + i, λ₂ = 1 - i Stable node OI and II = 2y1 - y2. OStable focus with 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: y₁ = y₁ − Y2, a) The corresponding eigenvalues are Oλ₁ = 1, λ₂ = −1 b) The corresponding eigenvectors of this linear ODE system are: OI and IV Oll and III OllI and IV where I:u₁ = II:u₂ = III:u₁ IV:u₂ 1+i 2 (¹3²) Oλ₁ = i, λ₂ = −i = ( 2 (1 + i)) • (20²+0) = 2(1 + i) c) The phase portrait for this system of ODEs is OCentre OUnstable focus with spiral out Oλ₁=1+i, λ₂ = 1-i Stable node y₂ = 2y₁ - y2. OI and II OStable focus with spiral in
Transcribed Image Text:Consider a system of two linear first-order ordinary differential equations: y₁ = y₁ − Y2, a) The corresponding eigenvalues are Oλ₁ = 1, λ₂ = −1 b) The corresponding eigenvectors of this linear ODE system are: OI and IV Oll and III OllI and IV where I:u₁ = II:u₂ = III:u₁ IV:u₂ 1+i 2 (¹3²) Oλ₁ = i, λ₂ = −i = ( 2 (1 + i)) • (20²+0) = 2(1 + i) c) The phase portrait for this system of ODEs is OCentre OUnstable focus with spiral out Oλ₁=1+i, λ₂ = 1-i Stable node y₂ = 2y₁ - y2. OI and II OStable focus with spiral in
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