a) Which of the following systems of ODEs is autonomous and dynamical? || III, where 1:y₁ = e sin(y₂), y2 = y1 + y2 dy₂ 11: = 5y1, dy₁ dx dx III: y₁' = 3y2, = -Y2 Y2Y1Y2Y/2 b) Find out which of the following options are equilibria of the dynamical system, IV 1 where I: (y₁, y) = (5, 0); II:(y†, y₂) = (3,0); III:(y₁, y) = (0, 1); IV:(y†, y₂) = (3, 2). y₁ = ₁²1, y2 = (y₁ - 3)2
a) Which of the following systems of ODEs is autonomous and dynamical? || III, where 1:y₁ = e sin(y₂), y2 = y1 + y2 dy₂ 11: = 5y1, dy₁ dx dx III: y₁' = 3y2, = -Y2 Y2Y1Y2Y/2 b) Find out which of the following options are equilibria of the dynamical system, IV 1 where I: (y₁, y) = (5, 0); II:(y†, y₂) = (3,0); III:(y₁, y) = (0, 1); IV:(y†, y₂) = (3, 2). y₁ = ₁²1, y2 = (y₁ - 3)2
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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Transcribed Image Text:a) Which of the following systems of ODEs is autonomous and dynamical?
III,
II
where
1: y₁= e = sin(y2), y2 = ₁ + y2
II: dy
dy₁
dx
dy₂
= 5y₁, y =
dx
Y₂' = V1 Y2 - y2
1
III: Y1 = Зуг,
= -12
b) Find out which of the following options are equilibria of the dynamical system,
IV
where I:(y₁, y) = (5,0); II:(y₁, y₂) = (3,0);
III:(y₁, y) = (0, 1); IV:(y₁, y) = (3,2).
y₁ = ₁₂ - 1, y2 = (y₁ - 3)y2
=
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