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a) Which of the following systems of ODES is autonomous and dynamical? OIII, Oll where 1:y₁' = 3y₁, y2 = y1 - y2 ||: Y₁ = y2e³¹ − In(1+|y2|), y2 = (Y₁Y2)5/2 - III:₁ = ln(3+|y₁|), da dy2 dr = -Y2 b) Find out which of the following options are equilibria of the dynamical system, y₁ = 1/2-1-1, y2 = (1-4)32 OIV Olll where I: (y₁, y) = (1, 0); II: (y₁, y₂) = (4, 0); III: (y₁, y) = (4, 1/4); IV:(y₁, y₂) = (1,1). Oll

a) Which of the following systems of ODES is autonomous and dynamical? OIII, Oll where 1:y₁' = 3y₁, y2 = y1 - y2 ||: Y₁ = y2e³¹ − In(1+|y2|), y2 = (Y₁Y2)5/2 - III:₁ = ln(3+|y₁|), da dy2 dr = -Y2 b) Find out which of the following options are equilibria of the dynamical system, y₁ = 1/2-1-1, y2 = (1-4)32 OIV Olll where I: (y₁, y) = (1, 0); II: (y₁, y₂) = (4, 0); III: (y₁, y) = (4, 1/4); IV:(y₁, y₂) = (1,1). Oll

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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a) Which of the following systems of ODES is autonomous and dynamical? OIII, where 1:y₁' = 3y₁, y2 = y1 - y2 ||: Y₁ = y2e³¹ − In(1+|y2|), y2 = (Y₁Y2)5/2 - III:₁ = ln(3+|y₁|), da dy2 da = -Y2 b) Find out which of the following options are equilibria of the dynamical system, y₁ = ₁/2-1-1, y2 = (1-4)32 OIV Olll where I: (y₁, y) = (1, 0); II: (y₁, y₂) = (4, 0); III: (y₁, y) = (4, 1/4); IV:(y₁, y₂) = (1,1). Oll
Transcribed Image Text:a) Which of the following systems of ODES is autonomous and dynamical? OIII, where 1:y₁' = 3y₁, y2 = y1 - y2 ||: Y₁ = y2e³¹ − In(1+|y2|), y2 = (Y₁Y2)5/2 - III:₁ = ln(3+|y₁|), da dy2 da = -Y2 b) Find out which of the following options are equilibria of the dynamical system, y₁ = ₁/2-1-1, y2 = (1-4)32 OIV Olll where I: (y₁, y) = (1, 0); II: (y₁, y₂) = (4, 0); III: (y₁, y) = (4, 1/4); IV:(y₁, y₂) = (1,1). Oll
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