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a) Which of the following systems of ODEs is autonomous and dynamical? OIII, where 1: y₁ = e sin(y₂), y2 = ₁ + y2 - ||: y = 5y₁, =-Y2 dy2 dx dx III: y₁' = 3y2, Y2' = V1 Y2 - y2 Oll b) Find out which of the following options are equilibria of the dynamical system, y₁=e121, OIV where I: (y₁, y) = (5,0); II:(y₁, y) = (3,0); III: (y₁, y) = (0, 1); IV:(y₁, y) = (3,2). Olll y2 = (y₁ - 3)y2 Oll

a) Which of the following systems of ODEs is autonomous and dynamical? OIII, where 1: y₁ = e sin(y₂), y2 = ₁ + y2 - ||: y = 5y₁, =-Y2 dy2 dx dx III: y₁' = 3y2, Y2' = V1 Y2 - y2 Oll b) Find out which of the following options are equilibria of the dynamical system, y₁=e121, OIV where I: (y₁, y) = (5,0); II:(y₁, y) = (3,0); III: (y₁, y) = (0, 1); IV:(y₁, y) = (3,2). Olll y2 = (y₁ - 3)y2 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 = e³¹ - sin(y₂), dy2 dx y₂ = y₁ + y2 dy1 II: = 5y₁, = -12 dx III: y₁ = 3y2, Y2 = V₁ Y2 - Y2 b) Find out which of the following options are equilibria of the dynamical system, y₁ = e³1³2 - 1, OIV where I: (y₁, y) = (5, 0); II:(y₁, y) = (3,0); III:(y†, yž) = (0, 1); IV:(y†, yž) = (3, 2). Oll y2 = (y₁ - 3)y2 Ō
Transcribed Image Text:a) Which of the following systems of ODEs is autonomous and dynamical? OIII, where 1: y₁ = e³¹ - sin(y₂), dy2 dx y₂ = y₁ + y2 dy1 II: = 5y₁, = -12 dx III: y₁ = 3y2, Y2 = V₁ Y2 - Y2 b) Find out which of the following options are equilibria of the dynamical system, y₁ = e³1³2 - 1, OIV where I: (y₁, y) = (5, 0); II:(y₁, y) = (3,0); III:(y†, yž) = (0, 1); IV:(y†, yž) = (3, 2). Oll y2 = (y₁ - 3)y2 Ō
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