Results 1 to 3 of 3

Math Help - state whether the system is homogeneous or not.

  1. #1
    Member
    Joined
    Oct 2010
    Posts
    127

    state whether the system is homogeneous or not.

    After working on a problem, I found out the system to be: x_1' = x_2 and x_2'=-25x_1+10x_2. I can figure out this is autonomous because the right side of the equation does not explicitly depend on the variable t. But how do reason whether it's homogeneous or not? Thanks.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    It is homogeneous, because there are no functions present that do not depend on x1 or x2. Here's an inhomogeneous system: x_1' = x_2 + t and x_2'=-25x_1+10x_2.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,393
    Thanks
    1327
    You start, as Ackbeet did, from the definition of "homogeneous". What is that?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Delay in a state-space system...
    Posted in the Advanced Applied Math Forum
    Replies: 7
    Last Post: March 15th 2011, 02:35 PM
  2. Replies: 0
    Last Post: December 6th 2010, 04:20 PM
  3. Solutions for a homogeneous system
    Posted in the Algebra Forum
    Replies: 1
    Last Post: October 10th 2009, 09:41 PM
  4. Homogeneous Linear System
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: September 1st 2009, 07:48 PM
  5. Homogeneous system
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: May 27th 2009, 09:16 PM

Search Tags


/mathhelpforum @mathhelpforum