Exercise 3. (General Solution)Consider the system i = 4x – y, ÿ = 2x + y a) Write the system in matrix form, find the corresponding characteristic polynomial, and solve for the eigenvalues and eigenvectors. b) Find the general solution of the system of differential equations, c) Classify the fixed point at the origin. d) Solve the system with the initial condition xo 3 and yo = 4.
Exercise 3. (General Solution)Consider the system i = 4x – y, ÿ = 2x + y a) Write the system in matrix form, find the corresponding characteristic polynomial, and solve for the eigenvalues and eigenvectors. b) Find the general solution of the system of differential equations, c) Classify the fixed point at the origin. d) Solve the system with the initial condition xo 3 and yo = 4.
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:Exercise 3.
(General Solution)Consider the system i = 4x – y, ÿ = 2x + y
a) Write the system in matrix form, find the corresponding characteristic polynomial,
and solve for the eigenvalues and eigenvectors.
b) Find the general solution of the system of differential equations,
c) Classify the fixed point at the origin.
d) Solve the system with the initial condition xo = 3 and yo = 4.
Expert Solution

Step 1
Given system is
(i)
In matrix form, system (i) can be written as
(ii)
Where
In order to find eigenvalues and eigenvectors, let us solve corresponding characteristic equation of matrix A
For
On solving the matrix equation , taking gives . So, eigenvector corresponding to the eigenvalue is
For , corresponding eigenvector is
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