- #1
Euler2718
- 90
- 3
Homework Statement
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].
Homework Equations
The Attempt at a Solution
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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.