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Solving Matrix of Differential Equations With Initial Values

  1. Apr 20, 2012 #1
    1. The problem statement, all variables and given/known data
    Solve the matrix of differential equations with given initial values.

    dx/dt= (-6 2) x
    (-3 -1)

    Initial value is x(0) = -2
    -5

    2. Relevant equations

    (A-λI)=o


    3. The attempt at a solution

    My eigenvalues are -4 and 3

    My eigenvectors for -4 are 1 and 1 and the eigenvectors for -3 are 1 on the top row and 3/2 on the bottom.

    I write out the equations to look like:

    C1e^-4t + C2e^-3t
    C1e^-4t + 3/2C2e^-3t

    I have IVs of -2 on the top row and -5 on the bottom row. To plug these in correctly,do I use the top row values for the top row equation and same for the bottom? If so, I'm getting C1=4 and C2=-6 but this is wrong in our online homework program.
     
  2. jcsd
  3. Apr 20, 2012 #2
    I figured out what I was doing wrong. It was a matter of entering the answer into the online homework program incorrectly, not so much that the answers were wrong.
     
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