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Solving an ODE

  1. Jan 2, 2012 #1
    If I wanted to solve this [itex] y''+3iy'+y=cos(2t) [/itex] using undetermined coefficients.
    and I make the guess [itex] y=Ae^{2it} [/itex]
    then i find y' and y'' and then solve for A. I get that A=-1/9
    then I take the real part when I multiply it to Eulers formula.
    But when I plug this back in to check it doesn't work.
    Is there something weird going on because I have an imaginary coefficient in front of the y'.
     
  2. jcsd
  3. Jan 2, 2012 #2
    Better, try : y = A exp(2it) +B exp(-2it)
    with cos(2t) = (1/2)exp(2it) + (1/2)exp(-2it)
     
  4. Jan 2, 2012 #3
    How about even more better:

    [tex]y_p=A\cos(2t)+B\sin(2t)[/tex]

    slap it in (the DE), equate coefficients, bingo-bango.

    Also, nothing (algebraic) changes if not only the coefficients are complex but everything else like y and x are complex too. So don't let the i thing intimiate you. Just use regular ordinary complex arithemetic and muscle-through the algebra like always.
     
    Last edited: Jan 2, 2012
  5. Jan 3, 2012 #4
    okay thanks for the advice
     
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