$u'' + 0.125u' + u = 0$
I'm told to let $x_1 = u$ and $x_2 = u'$. Thus, $x_1' = x_2$ and $x_2' = u''$. Thus, we have:
$x_2' + 0.125x_2 + x_1 = 0$
Now here is where I get confused. The book says that $x_1$ and $x_2$ now satisfy the equations:
$x_1' = x_2$ and $x_2' = -x_1 - 0.125x_2$
Can someone elaborate on why this is the answer we're looking for? And how I can generalize this for differential equations of higher order?