Toronto Math Forum
Welcome,
Guest
. Please
login
or
register
.
1 Hour
1 Day
1 Week
1 Month
Forever
Login with username, password and session length
News:
Home
Help
Search
Calendar
Login
Register
Toronto Math Forum
»
MAT244-2018S
»
MAT244--Tests
»
Quiz-6
»
Q6--T0201
« previous
next »
Print
Pages: [
1
]
Author
Topic: Q6--T0201 (Read 1739 times)
Victor Ivrii
Administrator
Elder Member
Posts: 2563
Karma: 0
Q6--T0201
«
on:
March 16, 2018, 08:09:14 PM »
a.
Express the general solution of the given system of equations in terms of real-valued functions.
b.
Also draw a direction field, sketch a few of the trajectories, and describe the behavior of the solutions as $t\to \infty$.
$$\mathbf{x}' =\begin{pmatrix}
-2 &1\\
1 &-2
\end{pmatrix}\mathbf{x}$$
«
Last Edit: March 16, 2018, 08:10:48 PM by Victor Ivrii
»
Logged
Ge Shi
Jr. Member
Posts: 8
Karma: 3
Re: Q6--T0201
«
Reply #1 on:
March 17, 2018, 12:11:47 AM »
(a)
In the attachement
(b)
When t approaches to infinity, the solution is approaches to zero
Since $\lambda_1=-3$ , $\lambda_2=-1$
Eigenvalues are real but unequal and have the same sign, x=0 is a node and asymptotically stable.
«
Last Edit: March 17, 2018, 12:48:14 PM by Ge Shi
»
Logged
Victor Ivrii
Administrator
Elder Member
Posts: 2563
Karma: 0
Re: Q6--T0201
«
Reply #2 on:
March 17, 2018, 05:02:28 AM »
Do not use external images; they will disappear at some moment. Please attach to your post.
Also, please correct your post, instead of lambda1=-3 write \lambda_1=-3 and surround by dollar signs
Code:
[Select]
$\lambda_1=-3$
What s/w did you use for a plot?
«
Last Edit: March 17, 2018, 05:09:17 AM by Victor Ivrii
»
Logged
Print
Pages: [
1
]
« previous
next »
Toronto Math Forum
»
MAT244-2018S
»
MAT244--Tests
»
Quiz-6
»
Q6--T0201