Answer
$x_1'=x_2$
$x_2'=-0.5x_2-2x_1$.
Work Step by Step
The given equation is
$u''+0.5u'+2u=0$
Let $x_1=u$ and $x_2=u'$
We can write $x_1'=x_2$ and $u''=x_2'$
Substitute all values into the given equation.
$x_2'+0.5x_2+2x_1=0$
Hence, the conditions satisfy the given equation.
The first order differential equations are:
$x_1'=x_2$
$x_2'=-0.5x_2-2x_1$.
