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Math Help - complex exponentials.

  1. #1
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    complex exponentials.

    Using the complex exponential, find the most general function f such that


    f''(x) = e-3tcos (2t) , for t element of reals.

    Relevant equations:


    f''(x) is second derivative.


    Do i tackle this problem by taking the anti derivative of both sides, then doing it one more time to get
    f(x) = ............
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  2. #2
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    Re: complex exponentials.

    Yes, and using the fact that e^{-3t}cos(2t) is the real part of e^{(-3+ 2i)t} (that is the "complex exponential") makes it very easy.
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  3. #3
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    Re: complex exponentials.

    I still dont really get it is there any other way to help explain it? i did the first derivative and got down to
    1/13*e^(-3t) *( -3 cos2t + sin2t) + c

    What would be the next step or have i gone about it the hard way? thanks for your help.
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  4. #4
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    Re: complex exponentials.

    yeah it is easy all i had to do was square the (1/(-3+2i)) which is like integrating twice. I hope that's what you mean to do.
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