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Math Help - 2nd order of differential equation.

  1. #1
    Glb
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    2nd order of differential equation.

    y'' -3y + 2y = e^2ix

    Will this imaginary constant make some trouble for me?

    I have tried this

    Y = Ae2ix
    and the derivative of that
    Y' = 2Ae^2ix
    Y''= 4Ae^2ix

    I cant figure out how to get the full solution, because I already have the homogenous equation solved. what about this, what will be the constants?
    Last edited by mr fantastic; March 13th 2011 at 12:56 PM. Reason: Title.
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  2. #2
    Flow Master
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    Quote Originally Posted by Glb View Post
    y'' -3y + 2y = e^2ix

    Will this imaginary constant make some trouble for me?

    I have tried this

    Y = Ae2ix
    and the derivative of that
    Y' = 2Ae^2ix Mr F says: This is wrong. It should be 2iAe^2ix.
    Y''= 4Ae^2ix Mr F says: This is wrong too. It should be -4Ae^2ix.

    I cant figure out how to get the full solution, because I already have the homogenous equation solved. what about this, what will be the constants?
    Substitute the correct derivatives into the DE and simplify:

    -4A -6iA +2A = 1.

    Solve for A.
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