(c) Hence determine the type and stability of the equilibrium point Xe = 0. (d) Solve the initial value problem of x.
(c) Hence determine the type and stability of the equilibrium point Xe = 0. (d) Solve the initial value problem of x.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Needed to be solved Part C and D correctly in 10 minutes and get the thumbs up please show neat and clean work for it
![Consider the following initial value problem
*-* *-[2].
x(0)
=
4 7
1
dx
dt
X,
where x =
-
x₁(t)
x₂(t)
(a) Calculate the matrices B and G of the real canonical form
dy
dt
X= = Gy,
By.
(b) Sketch the phase portrait on the (y₁, y2) plane, displaying the
typical orbits and directions.
(c) Hence determine the type and stability of the equilibrium point
Xe = 0.
(d) Solve the initial value problem of x.
4](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0567139a-9f93-4ba8-a710-9c19173fc9d7%2F0878d53b-00ab-42be-ad71-cfc593339a55%2F5lzuk4o_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the following initial value problem
*-* *-[2].
x(0)
=
4 7
1
dx
dt
X,
where x =
-
x₁(t)
x₂(t)
(a) Calculate the matrices B and G of the real canonical form
dy
dt
X= = Gy,
By.
(b) Sketch the phase portrait on the (y₁, y2) plane, displaying the
typical orbits and directions.
(c) Hence determine the type and stability of the equilibrium point
Xe = 0.
(d) Solve the initial value problem of x.
4
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