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I Question about using matrices for differential equations

  1. Mar 31, 2016 #1
    Let x(t)=
    [x1(t)
    x2(t)]
    be a solution to the system of differential equations:

    x′1(t)=−2x1(t)+2x2(t)
    x′2(t)==−6x1(t)+9x2(t)

    If x(0)=
    [4
    -2]
    find x(t).

    I got the eigenvalues to be -6 and -5, but I don't know how to calculate the coefficients in front of the exponents. For lambda=-6 I get the vector (1, -2) and for lambda=-5 I get the vector (2, -3). I think these would be the coefficients, but I'm not sure, and I don't know how to use the initial values for x(0). Thanks for your help!
     
  2. jcsd
  3. Mar 31, 2016 #2

    micromass

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    Given a system of equations ##\dot{\mathbf{x}}(t) = A \mathbf{x}(t)##, what is the general solution of this problem?
     
  4. Mar 31, 2016 #3
    I put the vectors eigenvectors from into a matrix and put 4 and -2 on the right and solved for the two variables. I got -8 and 6 but the website says only -8 is right, and in don't know where to get the other two coefficients?
     
  5. Mar 31, 2016 #4

    micromass

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    That doesn't answer my question at all.
     
  6. Mar 31, 2016 #5
    Wouldn't it just be A? Since other than that both sides are the same?
     
  7. Mar 31, 2016 #6

    micromass

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    In your course, what does it tell you about systems of differential equations? What book are you reading?
     
  8. Mar 31, 2016 #7
    I haven't taken differential equations yet. I'm in matrix algebra using Elementary Linear Algebra 7e by Larson.
     
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