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Math Help - Determine a Dif EQ

  1. #1
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    Determine a Dif EQ

    For each of the following, determine a differential equation (or a system of Dif EQ's), which has the expression of what is below for the general sol'n.

    1.) y=c_1\cos(\sqrt{2}t)+c_2\sin(\sqrt{2}t)

    2.) y=c_1e^{4t}+c_2te^{4t}

    3.) \textbf{X}=c_1\left(\begin{array}{r}0\\1 \end{array}\right)e^{-3t}+c_2\left(\begin{array}{r} 1\\0 \end{array}\right)e^{2t}
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  2. #2
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    Let's think about characteristic equations:

    1) Imaginary Solutions?

    2) Real, Repeated Solutions?

    3) Real, Unequal solutions?
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  3. #3
    MHF Contributor kalagota's Avatar
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    Quote Originally Posted by Auxiliary View Post
    For each of the following, determine a differential equation (or a system of Dif EQ's), which has the expression of what is below for the general sol'n.

    1.) y=c_1\cos(\sqrt{2}t)+c_2\sin(\sqrt{2}t)
    \frac{d^2y}{dt^2} + 2y = 0

    Quote Originally Posted by Auxiliary View Post
    2.) y=c_1e^{4t}+c_2te^{4t}
    \frac{d^2y}{dt^2} - 8\frac{dy}{dt} + 16y = 0
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  4. #4
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    Quote Originally Posted by kalagota View Post
    \frac{d^2y}{dt^2} + 2y = 0



    \frac{d^2y}{dt^2} - 8\frac{dy}{dt} + 16y = 0
    Thanks kalagota! How exactly did you come up with those by the way? Was it a trial and error type of deal?
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  5. #5
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Auxiliary View Post
    Thanks kalagota! How exactly did you come up with those by the way? Was it a trial and error type of deal?
    Quote Originally Posted by kalagota View Post
    \frac{d^2y}{dt^2} + 2y = 0
    Let's turn this around for a moment:

    How would you go about solving
    \frac{d^2y}{dt^2} + 2y = 0

    Therein lies your answer...

    -Dan
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  6. #6
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    Quote Originally Posted by Auxiliary View Post
    Thanks kalagota! How exactly did you come up with those by the way? Was it a trial and error type of deal?
    Come on, Aux. there are nearly eyeball problems. You simply MUST read up on the characteristic equation. You can't be struggling here or you'll never make it.
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  7. #7
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    Heh, I do very well on the exams. In fact, I have an A in this course. This is just the harder practice that I choose to do as well. I see now that it was quite trivial, although the systems one will take some work.

    Thanks for the help.
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