Rewriting ODE's into lower orders

[Euler2718]

Homework Statement

Express

\frac{d^{2}x}{dt^{2}} + \sin(x) = 0

In a system in terms of x' and y'.

Homework Equations

The Attempt at a Solution

[/B]
I seen this example:

x^{\prime\prime\prime} = x^{\prime}(t)\cdot x(t) - 2t(x^{\prime\prime}(t))^{2}

Where they then wrote:

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

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:

x^{\prime} = y
y^{\prime} = x^{\prime\prime} = -\sin(x)

Not really familiar with ODE's and such processes, but I need to apply this correctly to proceed with my work.

 

[Mark44]

Homework Statement

Express

\frac{d^{2}x}{dt^{2}} + \sin(x) = 0

In a system in terms of x' and y'.

Homework Equations

The Attempt at a Solution

[/B]
I seen this example:

x^{\prime\prime\prime} = x^{\prime}(t)\cdot x(t) - 2t(x^{\prime\prime}(t))^{2}

Where they then wrote:

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

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:

x^{\prime} = y
y^{\prime} = x^{\prime\prime} = -\sin(x)

This is it right here.

 

[Euler2718]

This is it right here.

Thanks. I really had to be sure before continuing.