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Math Help - Writing a 2nd order ODE as a system of 1st order ODEs

  1. #1
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    Writing a 2nd order ODE as a system of 1st order ODEs

    First the 2nd order ODE,

    \frac{d^2u}{dt^2} = 5tu + \sin (d_tu)\qquad u(0)=1 \quad d_tu=0

    Now this is what I have done, however I have no way of checking so, am I right?

    \begin{align*} d_tu&=v\\d_tv&=5tu+\sin (v)\\w&=\left(\begin{array}{c}u\\ v\end{array}\right)\\ d_tw&=\left(\begin{array}{c}v\\ 5tu+\sin (v)\end{array}\right)\\w(0)&=\left(\begin{array}{c  }u(0)\\ v(0)\end{array}\right) = \left(\begin{array}{c}1\\ 0\end{array}\right)\end{align*}

    Thanks.
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  2. #2
    Junior Member
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    Re: Writing a 2nd order ODE as a system of 1st order ODEs

    Don't worry, I found out how to solve ODEs in Maple1 and confirmed that I was correct.

    1 - Solving Ordinary Differential Equations with Maple...
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