d(x) = (x+1)(-x-2y) dt dy dt (y+1) (2y-1²-2x) a) find all critical points 6) find the jacobi matrix and the linearisation of the System at (0,0) c) use eigenvalues & eigenvectors to find the general. solution of the linearived system at (0,0).
d(x) = (x+1)(-x-2y) dt dy dt (y+1) (2y-1²-2x) a) find all critical points 6) find the jacobi matrix and the linearisation of the System at (0,0) c) use eigenvalues & eigenvectors to find the general. solution of the linearived system at (0,0).
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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Question
Please help answer this question, thank you
Transcribed Image Text:d(x)
de
dy
at
a)
find all critical points
b) find the jacobi matrix and the linearisation of
เ
the System at (0,0)
c)
(x+1)(-x-2y)
= (y+1) (2y-k²-21₁)
e)
d) find
f
use eigenvalues & exgenvectors to find the general
solution of the linearived system at (0,0).
any straight line orbite & direction.
behaviour of the Orbits as +→00
behaviour of the Orbits as t→-00
find the slope when Orbits cross the coordinate axes.
phare portrait around (0,0)
Sketch a
Use PPLANE to sketch a
global phate portrait for the nonlinear
of -4≤x≤3
⑥ -3<y<4
show 4 orbits in the immediate vicinity of each critical point.
Vyrtem
if x(0) >0 & y(0) <0
from global phase portrant, what happens to xlt) and y(t) as t-ts.
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