Problem $2(18$ pts$)$

Rewrite the following second$-$order ordinary differential equations $($ODEs$)$ into a set of firstorder ODEs by changes of variables, $($a$)(4$ pts$)p_{1}x$ and $p_2{x}^{}$; and $($b$)(8$ pts$)q_{1}y,q_2{y}^{},q_3{y}^{},$ and $q_4{y}^{},$ respectively. Express the set of ODEs in a vector$-$matrix form. $(2+4pts)$

$($a$)$

$m{x}^{}+b{x}^{}+kx=F$

$($b$)$

$y^{}+y^{}+y^{}+y^{}+{}_n^{2}y=$