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Math Help - system of ODE

  1. #1
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    system of ODE

    Hi, Please can someone help me on how to do this exercise.


    Give a fundamental matrix for the system:
    {x'(t)=-y(t)
    {y'(t)=20x(t)-4y(t)


    the solution is like:
    {v1(t)=e^(2t)*cos(4t)[1;4]+e^(2t)*sin(4t)[-1;-2], v2(t)=e^(2t)*cos(4t)[1;4]+e^(2t)*sin(4t)[0;-4]}

    [1;4].......are colunm vectors.
    IT is just a form sample .since it is a multiple choice question, I just took one solution to show you what it might look like.

    Thank you,
    B
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by braddy
    Hi, Please can someone help me on how to do this exercise.


    Give a fundamental matrix for the system:
    {x'(t)=-y(t)
    {y'(t)=20x(t)-4y(t)


    the solution is like:
    {v1(t)=e^(2t)*cos(4t)[1;4]+e^(2t)*sin(4t)[-1;-2], v2(t)=e^(2t)*cos(4t)[1;4]+e^(2t)*sin(4t)[0;-4]}

    [1;4].......are colunm vectors.
    IT is just a form sample .since it is a multiple choice question, I just took one solution to show you what it might look like.

    Thank you,
    B
    Not sure this is what you need but the system is equivalent to:

    <br />
X'(t)=\left[  \begin{array}{cc}0 & -1\\20 & -4\end{array}   \right]X(t)<br />

    where X(t) and X'(t) are column vectors.

    RonL
    Last edited by CaptainBlack; April 25th 2006 at 04:20 AM.
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  3. #3
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    Quote Originally Posted by CaptainBlack
    Not sure this is what you need but the system is equivalent to:

    <br />
X'(t)=\left[  \begin{array}{cc}0 & -1\\20 & -4\end{array}   \right]X(t)<br />

    where X(t) and X'(t) are column vectors.

    RonL
    Ok I have trouble converting it into a system .
    Yes this is it . I know how to solve it.
    Thank you captain
    B
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by braddy
    Hi, Please can someone help me on how to do this exercise.


    Give a fundamental matrix for the system:
    {x'(t)=-y(t)
    {y'(t)=20x(t)-4y(t)


    the solution is like:
    {v1(t)=e^(2t)*cos(4t)[1;4]+e^(2t)*sin(4t)[-1;-2], v2(t)=e^(2t)*cos(4t)[1;4]+e^(2t)*sin(4t)[0;-4]}

    [1;4].......are colunm vectors.
    IT is just a form sample .since it is a multiple choice question, I just took one solution to show you what it might look like.

    Thank you,
    B
    It is of course also equivalent to the 2-nd order ODE:

    <br />
\ddot y(t)=-20y(t)+4\dot y(t)<br />

    or:

    <br />
\ddot y(t)-4\dot y(t)+20y(t)=0<br />

    RonL
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  5. #5
    Super Member Rebesques's Avatar
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    Yes this is it . I know how to solve it.

    Don't tell me you 'll go for e^{At}...
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