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Inhomogeniouse System

  1. Aug 26, 2010 #1
    Good afternoon!
    I have a strange results solving this problem.

    x'=[3,4;-1,-1]*x+[e^t;0], with init. cond. x(0)=[1;0].

    x'=Ax+(e^(mu*t))*b thus mu=1, b=[1;0]

    x(t)=(e^(mu*t))((mu*I-A)^-1)*b
    x(t)=e^t*(([mu,0;0,mu]-[3,4;-1,-1])^-1)*b=e^t*([-2,-4;1,2]^-1)*[1;0]
    But the problem is that [-2,-4;1,2]^-1 matrix is singular to working precision.

    ans =

    Inf Inf
    Inf Inf

    Is that some typo in the matrix or am I using the wrong way to solve this type of equations?

    Thank you very much for any ideas!

    Best regards,
    Alina
     
  2. jcsd
  3. Aug 26, 2010 #2
    Hello. Please refer to my article in http://www.voofie.com/concept/Mathematics/" [Broken]:

    http://www.voofie.com/content/18/solving-system-of-first-order-linear-differential-equations-with-matrix-exponential-method/" [Broken]

    What you really need is matrix exponential, instead of matrix inverse. You can find example in another article:

    http://www.voofie.com/content/19/a-worked-example-of-solving-system-of-first-order-linear-differential-equation/" [Broken]
     
    Last edited by a moderator: May 4, 2017
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