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Math Help - differential eq.

  1. #1
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    differential eq.

    Let y be the solution of the initial value problem  y''+2y'+2y=0, y(0)=0, y'(0)=6

    The maximum value of  y for  t>0 is?
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  2. #2
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    Using the characteristic equation we have:

    m^{2}+2m+2=0

    m_{1}=-1+i, \;\ m_{2}=-1-i

    This gives:

    e^{-x}(C_{1}cos(x)+C_{2}sin(x))

    Now, use your initial conditions and get C_{1}=0, \;\ C_{2}=6

    y=6e^{-x}sin(x)

    Now, what's the max value for x>0?. Graph it may help.

    Differentiate, set to 0 and solve for x.
    Last edited by galactus; November 24th 2008 at 06:39 AM.
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