a) Which of the following systems of ODES is autonomous and dynamical? where ty₁ = e-sin(₂), y₂ = ₁ + y₂ 11:=5y₁. =-y2 :y₁ = 3y2. y2 = 132-92 b) Find out which of the following options are equilibria of the dynamical system, 111 where 1:(.)=(5,0); 11:(. )=(3,0); III:-)=(0, 1): IV:(₁-x) =(3,2). ye-1, y = (y₁ - 3)2 IV

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Question

2

a) Which of the following systems of ODES is autonomous and dynamical?
where
1:₁ = e-sin(₂), ₂ = ₁ + y₂
11: = 5₁.
= -9₂
dx
:y₁ = 3y2, y2 = 9192-92
b) Find out which of the following options are equilibria of the dynamical system,
y₁ =
11
111
where 1:(₁.2)=(5,0); II:(,)=(3,0);
III:(.) = (0, 1): IV:(₁-x) =(3,2).
-1₁ y₂ = (1 - 3)2
CIV
Transcribed Image Text:a) Which of the following systems of ODES is autonomous and dynamical? where 1:₁ = e-sin(₂), ₂ = ₁ + y₂ 11: = 5₁. = -9₂ dx :y₁ = 3y2, y2 = 9192-92 b) Find out which of the following options are equilibria of the dynamical system, y₁ = 11 111 where 1:(₁.2)=(5,0); II:(,)=(3,0); III:(.) = (0, 1): IV:(₁-x) =(3,2). -1₁ y₂ = (1 - 3)2 CIV
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,