b) Find out which of the following options are equilibria of the dynamical system, y₁ = e²₁₂-¹ — 1, y2 = (y₁ - 4)y2 - OIII Oll OI OIV where I: (y₁, y₂) = (1,0); II:(y†, y₂) = (4, 0); III:(y₁, y₂) = (4, 1/4); IV:(y₁, y₂) = (1, 1).
b) Find out which of the following options are equilibria of the dynamical system, y₁ = e²₁₂-¹ — 1, y2 = (y₁ - 4)y2 - OIII Oll OI OIV where I: (y₁, y₂) = (1,0); II:(y†, y₂) = (4, 0); III:(y₁, y₂) = (4, 1/4); IV:(y₁, 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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Part a and b please.
Transcribed Image Text:b) Find out which of the following options
are equilibria of the dynamical system,
y₁ = e³₁92-1-1, y₂ = (y₁ −4)y2
Oll
OI
OIV
OIII
where I:(y₁, y) = (1,0);
II:(y₁, yž) = (4, 0);
III: (y₁, y) = (4,1/4);
IV:(y₁, y₂) = (1, 1).
Transcribed Image Text:a) Which of the following systems of ODEs is autonomous and dynamical?
Olll,
where
1: y₁' = 3y₁, Y₂'
= Y1Y2
||: Y₁ = y₂eª¹ − ln(1 +|y2|), _Y2 = (Y1Y2)5/2
|||:
In(3+|y₁|),
-Y2
dy₁
dx
=
dy2
dx
=
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