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Homework Help: 2nd order homogeneous equations complex root

  1. Sep 25, 2010 #1
    1. The problem statement, all variables and given/known data
    y'' -2y' +5y =0 , y(0)=1, y'(0)=1
    you get a complex root conjugate.

    2. Relevant equations
    y''=r^2 * e^(rt)

    3. The attempt at a solution
    I have in my notes sin(omega*t)e^(sigma *t), cos(omega *t)e^(sigma).
    I don't think i took down the notes properly, can anyone care confirm if this is right or wrong?
  2. jcsd
  3. Sep 25, 2010 #2


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    Homework Helper

    Yes your homogeneous solutions are sin(ωt)eσt and cos(ωt)eσt when the roots are in the form r=σ ± ωi with 'i' being the imaginary unit.
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