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Rewriting ODE's into lower orders

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  1. Nov 15, 2016 #1
    1. The problem statement, all variables and given/known data

    Express

    [tex] \frac{d^{2}x}{dt^{2}} + \sin(x) = 0 [/tex]

    In a system in terms of [itex]x'[/itex] and [itex]y'[/itex].

    2. Relevant equations


    3. The attempt at a solution

    I seen this example:

    [tex]x^{\prime\prime\prime} = x^{\prime}(t)\cdot x(t) - 2t(x^{\prime\prime}(t))^{2} [/tex]

    Where they then wrote:

    [tex] x^{\prime} = y [/tex]
    [tex] y^{\prime} = z [/tex]
    [tex] z^{\prime} = y^{\prime\prime} = x^{\prime\prime\prime} = x^{\prime}(t)\cdot x(t) - 2t(x^{\prime\prime}(t))^{2} [/tex]
    So:
    [tex] z^{\prime} = xy - 2tz^{2} [/tex]
    Since [itex]y^{\prime\prime} = x^{\prime} = z[/itex]

    And thus an Euler's method can be devised in MATLAB, given some IVP's of course. Is this then the correct approach for my problem:

    [tex] x^{\prime} = y [/tex]
    [tex] y^{\prime} = x^{\prime\prime} = -\sin(x) [/tex]

    Not really familiar with ODE's and such processes, but I need to apply this correctly to proceed with my work.
     
  2. jcsd
  3. Nov 15, 2016 #2

    Mark44

    Staff: Mentor

    This is it right here.
     
  4. Nov 15, 2016 #3
    Thanks. I really had to be sure before continuing.
     
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