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Math Help - [SOLVED] Verify solution for 2nd order eqn. by taking real part....

  1. #1
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    [SOLVED] Verify solution for 2nd order eqn. by taking real part....

    Find the particular solutions of y_{p}(t) for the DEs:
    y''+B^{2}y=cos(wt) and
    y''+B^{2}y=sin(wt)
    by taking both the real and imaginary parts of the solution:
    z_{p}=\dfrac{sin((w-B)\dfrac{t}{2})}{(w-B)\dfrac{1}{2}}   \dfrac{e^{i(w+B)\dfrac{t}{2}}}{i(w+B)}
    Verify the solution for for: y''+B^{2}y=cos(wt)

    Just to clarify, all other variables except i are real numbers.

    Well, here is what i tried...
    I started of by trying to take the Real part of z_{p}, as the directions state. I think i can do it fine until i get to the denominator on the right side. Once i take the real part of i(w+b), it makes the demoninator zero, which leaves me stuck.

    Any helps would be be GREAT!
    Last edited by snaes; April 4th 2010 at 09:42 PM. Reason: small error...b's vs. B's
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  2. #2
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    Take the i out from the denominator by multiplying top and bottom by i to get:

    -i\left(\frac{\sin((w-b)t/2)e^{i(w-b)t/2}}{(w-b)(w+b)}\right)

    Now, when you expand the exponent you'll get an x+iy term which when multiplied by the i gives you a real component.
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  3. #3
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    Thanks, I got it figured out now.
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