Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
What type of fixed point is the equilibrium solution x = y = 0? Sketch the phase portrait of the linear system. Find the solution of the linear system corresponding to the initial conditions x(0) = 1, y(0) = 0. Determine the values limt→∞ x(t) and limt→∞ y(t).

What type of fixed point is the equilibrium solution x = y = 0? Sketch the phase portrait of the linear system. Find the solution of the linear system corresponding to the initial conditions x(0) = 1, y(0) = 0. Determine the values limt→∞ x(t) and limt→∞ y(t).

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

ONLY C & D

Consider a system of two nonlinear first-order ODEs, where x and y are functions of the independent variable t: 1 x = 2 tanh(x) — 2x cos(y) + ex+³y - 1, y = 3 cosh(x) — 3ey + 1 29+ sin(x). = (a) Write down in matrix form of the type X = AX with X (x, y) the system obtained by linearisation of the above equations around the point x = y = 0. Specify the elements of the matrix A. (b) Find the eigenvalues and eigenvectors of the matrix A obtained in (a). Write down the general solution of the linear system. (c) What type of fixed point is the equilibrium solution x = y = 0? Sketch the phase portrait of the linear system. (d) Find the solution of the linear system corresponding to the initial conditions x(0) = 1, y(0) = 0. Determine the values limt→∞ ä(t) and limt→∞ y(t).
Transcribed Image Text:Consider a system of two nonlinear first-order ODEs, where x and y are functions of the independent variable t: 1 x = 2 tanh(x) — 2x cos(y) + ex+³y - 1, y = 3 cosh(x) — 3ey + 1 29+ sin(x). = (a) Write down in matrix form of the type X = AX with X (x, y) the system obtained by linearisation of the above equations around the point x = y = 0. Specify the elements of the matrix A. (b) Find the eigenvalues and eigenvectors of the matrix A obtained in (a). Write down the general solution of the linear system. (c) What type of fixed point is the equilibrium solution x = y = 0? Sketch the phase portrait of the linear system. (d) Find the solution of the linear system corresponding to the initial conditions x(0) = 1, y(0) = 0. Determine the values limt→∞ ä(t) and limt→∞ y(t).
Expert Solution
steps

Step by step

Solved in 3 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
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,
SEE MORE TEXTBOOKS