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Consider a system of two linear first-order ordinary differential equations: y₁ = y2, y₂ = −9y₁. a) The corresponding eigenvalues are A₁ = 3, λ₂ = −3 b) The corresponding eigenvectors of this linear ODE system are II and III I and IV where I:U₂ = (3) 1 II:u₂ = III:u₁ = IV:u₁ = -3i 1 3i 3i -1 A₁ = 3i, λ₂ = -3i c) The phase portrait for this system of ODEs is Unstable focus with spiral out I and III Stable focus with spiral in ₁9, 1₂-9 I and III Stable node Centre

Consider a system of two linear first-order ordinary differential equations: y₁ = y2, y₂ = −9y₁. a) The corresponding eigenvalues are A₁ = 3, λ₂ = −3 b) The corresponding eigenvectors of this linear ODE system are II and III I and IV where I:U₂ = (3) 1 II:u₂ = III:u₁ = IV:u₁ = -3i 1 3i 3i -1 A₁ = 3i, λ₂ = -3i c) The phase portrait for this system of ODEs is Unstable focus with spiral out I and III Stable focus with spiral in ₁9, 1₂-9 I and III Stable node Centre

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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= y2, Consider a system of two linear first-order ordinary differential equations: y₁ a) The corresponding eigenvalues are A₁ = 3, 1₂ = −3 b) The corresponding eigenvectors of this linear ODE system are I and IV II and III where I:u₂ = II:u₂ III:u₁ IV:u₁ (3₁) (-3₁) (3) = (³1) 3i 3i = = λ₁ = 3i, λ₂ = -3i c) The phase portrait for this system of ODEs is Unstable focus with spiral out I and III Stable focus with spiral in y2 = -9y₁. ₁9, λ₂ = -9 I and III Stable node Centre
Transcribed Image Text:= y2, Consider a system of two linear first-order ordinary differential equations: y₁ a) The corresponding eigenvalues are A₁ = 3, 1₂ = −3 b) The corresponding eigenvectors of this linear ODE system are I and IV II and III where I:u₂ = II:u₂ III:u₁ IV:u₁ (3₁) (-3₁) (3) = (³1) 3i 3i = = λ₁ = 3i, λ₂ = -3i c) The phase portrait for this system of ODEs is Unstable focus with spiral out I and III Stable focus with spiral in y2 = -9y₁. ₁9, λ₂ = -9 I and III Stable node Centre
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