My Math Forum  

Go Back   My Math Forum > College Math Forum > Calculus

Calculus Calculus Math Forum

LinkBack Thread Tools Display Modes
January 4th, 2019, 10:25 AM   #1
Joined: Jan 2019
From: Croatia

Posts: 2
Thanks: 0

Stability of differential equation

Hi, I have big problem with solving one of exercises in my analysis course and I will be glad for any help.
I have ordinary differential equation:

and I have to examine stability of the above system.
I don't know even how to start - could someone explain me what the matrix means (normally I had equation like y'(x) + y(x) + 5x = 7 - maybe harder, but in one line, I see matrix first time) and how to start with this problem (examining stability)?

Last edited by skipjack; January 6th, 2019 at 02:49 AM.
kk11 is offline  
January 4th, 2019, 12:51 PM   #2
Global Moderator
Joined: May 2007

Posts: 6,763
Thanks: 697

You have two simultaneous equations. $Dy_1=-2y_1+3y_2+x^{-2}$ and $Dy_2=3y_1+y_2+x^{-2}$.
mathman is offline  
January 5th, 2019, 06:53 AM   #3
Senior Member
Joined: Sep 2016
From: USA

Posts: 619
Thanks: 391

Math Focus: Dynamical systems, analytic function theory, numerics
This is just a standard linear differential question. Generically, these are equations of the form'
\[y' = A(x)y + F(x)\]
where $A$ is a matrix and $y, F$ are vectors. This should be covered in a first course on differential equations. If not, then you really can't even parse the question much less answer it.

Now, your question as stated doesn't make sense. Differential equations don't have a stability. Stability is a property possessed by invariant sets which are unions of trajectories for a differential equation. Most commonly, you look at a single trajectory such as an equilibrium or a periodic solution. You need to rephrase your question before anyone can understand how to answer it.
SDK is offline  
January 5th, 2019, 08:17 AM   #4
Joined: Jan 2019
From: Croatia

Posts: 2
Thanks: 0

Thanks a lot for an answer. The problem is I can't add much more, I have just said:

Consider the system of the ordinary differential equations:

--here exactly what is on the picture--

Examine the stability of the above system.

Last edited by skipjack; January 6th, 2019 at 02:45 AM.
kk11 is offline  

  My Math Forum > College Math Forum > Calculus

differencial, differential, equasion, equation, stability

Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
Show that an equation satisfies a differential equation PhizKid Differential Equations 0 February 24th, 2013 10:30 AM
stability and unstability kernel Physics 4 August 26th, 2012 04:45 PM
stability improvement of equation system a_kamali Linear Algebra 0 August 15th, 2011 05:16 AM
Equilibria and their Stability Canucks89 Calculus 1 February 25th, 2008 12:54 PM
Non-Autonomous Differential Equation Stability, Please Help kaisersoze Differential Equations 0 December 16th, 2007 08:45 AM

Copyright © 2019 My Math Forum. All rights reserved.