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Homogeneous ODE system, how to solve using WOLFRAM

  1. Dec 8, 2012 #1
    Hi.

    If I have a homogeneous ODE with constant coefficient system in the form of 2x2 matrix:

    X'=A X, A is a 2x2 matrix.

    How do I solve this using wolfram or matlab?
     
  2. jcsd
  3. Dec 8, 2012 #2
    What is the system explicitly?
     
  4. Dec 8, 2012 #3
    Say

    X'= [2, 4] X.
    [1, 1]

    A with with 2,4 in the top rows, and 1,1 in the bottom rows.

    How do I use wolfram or matlab to solve this system?
     
  5. Dec 8, 2012 #4
    We can re-write the system as
    \begin{alignat*}{5}
    x' & = & 2x+4y & = & 0\\
    y' & = & x + y & = & 0
    \end{alignat*}

    DSolve[{x'[t]==2x[t]+4y[t],y'[t]==x[t]+y[t], Initial Conditions here},{x[t],y[t]},t]
     
  6. Dec 8, 2012 #5

    Ray Vickson

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    Science Advisor
    Homework Helper

    I do not have access to Matlab, so I don't know the answer to the following: does Matlab have a exp(A) function for a matrix A? If so, we have X(t) = X(0) exp(A*t).
     
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