How do i transform this:
$\frac{(d^2\theta)}{(dt^2)}(t) = -\frac{g}{L}sin(\theta(t))$
Where g and L are constants
to these two first order differential equations:
1) $\frac{dv}{dt} = -gsin(\theta)$
2) $\frac{d\theta}{dt} = \frac{1}{L}v$
knowing that:
$v(t) = L\frac{d\theta}{dt}(t)$
Since you know that $$ v(t)=L\frac {d\theta}{dt}$$ Your second equation is found by solving the above equation for $\frac{d\theta}{dt}$
The first equation is then found by differentiating the given equation and substitutin for $ \frac {d^2\theta}{dt^2} $ from your original second order equation .