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Consider a system of two linear first-order ordinary differential equations: y₁ = y₁ - y2, y₂ = 2y₁ - y2. Y1 a) The corresponding eigenvalues are O₁ = 1, ₁ = 1+i, Oλ₁ = i, A₂ = −1 A₂ = 1 - i 1₂ = -i b) The corresponding eigenvectors of this linear ODE system are: Oll and III OI and II OIII and IV OI and IV where I:U₁ = II:u2 1+i 2 2 (¹) (²3 (26² (2(₁1²+-+)) 2i 2(1 + i) i) = III:u₁= IV:u₂ =

Consider a system of two linear first-order ordinary differential equations: y₁ = y₁ - y2, y₂ = 2y₁ - y2. Y1 a) The corresponding eigenvalues are O₁ = 1, ₁ = 1+i, Oλ₁ = i, A₂ = −1 A₂ = 1 - i 1₂ = -i b) The corresponding eigenvectors of this linear ODE system are: Oll and III OI and II OIII and IV OI and IV where I:U₁ = II:u2 1+i 2 2 (¹) (²3 (26² (2(₁1²+-+)) 2i 2(1 + i) i) = III:u₁= IV:u₂ =

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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Part a,b and c please
Consider a system of two linear first-order ordinary differential equations: y₁ = y₁ - y2, ý₂ = 2y₁ - y2. Y1 a) The corresponding eigenvalues are O₁ = 1, ₁ = 1+i, Ολι Oλ₁ = i, A₂ = −1 A₂ = 1 - i 1₂ = -i b) The corresponding eigenvectors of this linear ODE system are: Oll and III OI and II OIII and IV OI and IV where I:U₁ II:u2 = 1+i 2 (¹) (²3 = III:u₁= IV:u₂ = 2 2i 2(1 + i) (2(₁1²+-+)) i)
Transcribed Image Text:Consider a system of two linear first-order ordinary differential equations: y₁ = y₁ - y2, ý₂ = 2y₁ - y2. Y1 a) The corresponding eigenvalues are O₁ = 1, ₁ = 1+i, Ολι Oλ₁ = i, A₂ = −1 A₂ = 1 - i 1₂ = -i b) The corresponding eigenvectors of this linear ODE system are: Oll and III OI and II OIII and IV OI and IV where I:U₁ II:u2 = 1+i 2 (¹) (²3 = III:u₁= IV:u₂ = 2 2i 2(1 + i) (2(₁1²+-+)) i)
c) The phase portrait for this system of ODEs is O Stable Stable focus with node spiral in OUnstable focus with spiral out O Centre
Transcribed Image Text:c) The phase portrait for this system of ODEs is O Stable Stable focus with node spiral in OUnstable focus with spiral out O Centre
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