Answer
See below
Work Step by Step
Given
$y''+ay'+by=F(t)$
We introduce new variables $x_1$ and $x_2$ defined by
$x_1=y\\
x_2=\frac{dy}{dt}$
Then the given differential equation can be replaced by the first-order system
$\frac{dx_2}{dt}+ax_2+bx_1=F(t)\\
x_2=\frac{dx_1}{dt}$
