a) Which of the following systems of ODEs is autonomous and dynamical? OIII, where 1: y₁' = 3y₁, Y2' = Y₁ - Y2 ||: y₁ = y₂e³¹ — ln(1 + [y₂]), _Y₂ = (Y1Y₂) 5/2 III: d = -12 dx : In(3 + |y₁|), = dy₂ dx b) Find out which of the following options are equilibria of the dynamical system, y₁ = e³₁³2-1 − 1, y₂ = (y₁ – 4)y₂ OIV where I:(y, y) = (1, 0); II:(y†, yž) = (4, 0); III:(y₁, yž) = (4, 1/4); IV:(y†, yž) = (1, 1). |||| 011
a) Which of the following systems of ODEs is autonomous and dynamical? OIII, where 1: y₁' = 3y₁, Y2' = Y₁ - Y2 ||: y₁ = y₂e³¹ — ln(1 + [y₂]), _Y₂ = (Y1Y₂) 5/2 III: d = -12 dx : In(3 + |y₁|), = dy₂ dx b) Find out which of the following options are equilibria of the dynamical system, y₁ = e³₁³2-1 − 1, y₂ = (y₁ – 4)y₂ OIV where I:(y, y) = (1, 0); II:(y†, yž) = (4, 0); III:(y₁, yž) = (4, 1/4); IV:(y†, yž) = (1, 1). |||| 011
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?
OIII,
|||
where
1: yı' = 3y₁, Y₂' = y₁ - y2
J1
II: y₁ = y₂e³¹ - ln(1 + y₂),
y₂ = (y₁ y2) 5/2
Y2 (Y1
dy2
|||: ₁ = ln(3+|y₁|), ² = -2
dx
dx
b) Find out which of the following options are equilibria of the dynamical system,
y₁ = e³1³2−¹ – 1,
OIV
where I:(y₁, y₂) = (1, 0); II:(y†, y₂) = (4,0);
III:(y†, y₂) = (4, 1/4); IV:(y†, yž) = (1, 1).
✔|||
y2 = (y₁ - 4)y₂
Oll
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