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Homework Help: Roots of a ODE

  1. Aug 31, 2007 #1
    y'' + 2y' + 5y = 0 (*)

    OK, what I have done is computing the two roots y1 = exp(-x)*cos2x and y2 = exp(-x)*sin2x.

    However, when I compute the derivatives of these two, and substitute into (*), the eq. doesn't equate 0.

    Are my roots wrong?
     
  2. jcsd
  3. Sep 1, 2007 #2

    Dick

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    In that case you haven't taken the derivatives correctly, because the roots are correct.
     
  4. Sep 1, 2007 #3
    Let us first look at the characteristic equation of the ODE.

    [tex]P(\lambda) = \lambda^2 + 2\lamda + 5 = 0[/tex]
    [tex](\lambda + 1)^2 = -4[/tex]
    [tex]\lambda + 1 = \pm2i[/tex]
    [tex]\lambda = -1 \pm2i[/tex]

    Your roots appear to be correct.
     
  5. Sep 1, 2007 #4
    Yes...

    The derivative of cos2x is -2sin2x, isn't it? I'm gonna check this tomorrow. Now I need some sleep.
     
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