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Homework Help: 2rd order ODE

  1. Oct 15, 2006 #1
    Solve the given initial value problem.
    9y"-12y'+4y=0 y(0)=2 y'(0)=-1

    9r^2-12r +4=0
    (3r-2)^2
    so r=2/3
    so my general solution would be y(t)=c_1e^2/3t +c_2e^2/3t
    Whenever I try to use the initial conditions I can't get them to work. One disappears.
    Is my general solution even right?
     
  2. jcsd
  3. Oct 15, 2006 #2

    StatusX

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    You only have one linearly independent solution there. When you get a double root like that, the other solution is given by, in this case, [itex]t e^{2/3 t} [/tex]. You can verify this by plugging it into the DE.
     
  4. Oct 15, 2006 #3
    I get it.. thanks a lot!!
     
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