a) Which of the following systems of ODES is autonomous and dynamical? OI Oll OIII, where 1:y₁ = 3y₁, y2 = y₁ - y2 ||: y₁ = y₂e³¹ — ln(1 +|y2|), y2 = (y₁y2) 5/2 - =-Y2 III: = ln(3 + |31), dy₁ da dy₂ dx b) Find out which of the following options are equilibria of the dynamical system, y₁ = e192-1-1, y2 = (y₁ - 4)y2 Oll OIII OIV where I: (yi, y) = (1, 0); II: (y1, y2) = (4,0); III: (y₁, y2)=(4, 1/4); IV:(y, y₂) = (1, 1).
a) Which of the following systems of ODES is autonomous and dynamical? OI Oll OIII, where 1:y₁ = 3y₁, y2 = y₁ - y2 ||: y₁ = y₂e³¹ — ln(1 +|y2|), y2 = (y₁y2) 5/2 - =-Y2 III: = ln(3 + |31), dy₁ da dy₂ dx b) Find out which of the following options are equilibria of the dynamical system, y₁ = e192-1-1, y2 = (y₁ - 4)y2 Oll OIII OIV where I: (yi, y) = (1, 0); II: (y1, y2) = (4,0); III: (y₁, y2)=(4, 1/4); IV:(y, y₂) = (1, 1).
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?
Oll
Olll,
where
1: y₁' = 3y₁, y₂ = Y₁ - Y2
Y2'
||: y₁ = y₂e³¹ - In(1 + y2), y2 = (y₁y2) 5/2
dy₁
dy₂
|||: = ln(3 + |y₁|), = -Y2
dx
dx
b) Find out which of the following options are equilibria of the dynamical
system,
y₁ = ³12-11, y2 = (y₁ - 4)y2
Oll
OIII
OIV
where I: (y1, y) = (1, 0); II: (y₁, y₂) = (4,0);
III:(y₁, y) = (4, 1/4); IV:(y₁, y₂) = (1,1).
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