Conversion into a system of differential equations

Why are systems of differential equations interesting? First of all many applications can be seen as a system of differential equations. As a first example we will see that this holds for a mass spring system.
And secondly we can convert higher order equations to a system of differential equations. These systems are easier to analyze than the original higher order equations.
And thirdly when solving differential equations numerically you have to convert them to systems of differential equations in order to use standard solvers in packages. So enough reasons to look into these systems. But how do we do this conversion? Fortunately that is easy, as you will see in this video.