Results 1 to 3 of 3

Math Help - stability of the differential equation

  1. #1
    Junior Member sweet's Avatar
    Joined
    Jan 2006
    Posts
    30

    stability of the differential equation

    hi all

    how can i discuss the stability of the D.E
    <br />
d^2x /dt^2 +alpha(alpha - 1) dx /dt + (pita - 1)(pita-2) x=0<br /> <br />

    thankx 4 help me
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by sweet View Post
    hi all

    how can i discuss the stability of the D.E
    <br />
d^2x /dt^2 +alpha(alpha - 1) dx /dt + (pita - 1)(pita-2) x=0<br /> <br />

    thankx 4 help me
    I know there is some cool way of doing stability problems.
    I can just solve it.
    y''+\alpha(\alpha -1)y'+(\rho -1)(\rho -2)x=0
    Reduction of order,
    u=y'
    u'+\alpha (\alpha -1)u+(\rho-1)(\rho-2)x=0
    u'+\alpha (\alpha -1)u=-(\rho-1)(\rho-2)x
    The integrating factor is,
    \mu(x)=\exp \left( \int \alpha (\alpha -1) dx\right)=\exp(\alpha (\alpha -1)x)
    Thus, when we solve this differencial equation,
    u=e^{-\alpha(\alpha-1) x}\int ......... dx
    Thus, for stability we need that,
    \alpha(\alpha-1)>0
    \alpha^2-\alpha >0
    \alpha^2-\alpha+\frac{1}{4}>\frac{1}{4}
    (\alpha-1/2)^2>1/4
    \alpha-1/2>1/2 \mbox{ or }\alpha -1/2<-1/2
    \alpha>1 \mbox{ or }\alpha <0

    BUT DO NOT RELY ON THIS. I just happend to know that the most important part in this is the exponential which is what I worked with.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member sweet's Avatar
    Joined
    Jan 2006
    Posts
    30
    thank u ThePerfectHacker

    but i need to study the stability in each piont of the ]0,1[
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Stability of Critical Points of Second Order Equation
    Posted in the Differential Equations Forum
    Replies: 3
    Last Post: December 7th 2011, 12:24 PM
  2. Replies: 4
    Last Post: May 8th 2011, 12:27 PM
  3. Proving Stability and Asymptotic Stability of Homogeneous Equations
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: November 4th 2010, 12:16 PM
  4. characteristic equation and stability
    Posted in the Advanced Applied Math Forum
    Replies: 1
    Last Post: May 8th 2009, 10:09 PM
  5. Stability
    Posted in the Advanced Applied Math Forum
    Replies: 0
    Last Post: January 17th 2007, 07:54 AM

Search Tags


/mathhelpforum @mathhelpforum