Without solving it, rewrite the given second order differential equation $$t^2u''+2.5tu' + (t^2 + 5)u = 7\sin(3t)$$ as an equivalent system of first order differential equations. In your answer use the single letter u to represent the function $u$ and the single letter v to represent the "velocity function" $u'$. Do not $u(t)$ or $v(t)$ to represent these functions. Expressions like $\sin(t)$ that represent other functions are OK.

$u' =$
$v' =$

Now write the system using matrices:

$\displaystyle \frac{d}{dt}$

$\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$ $u$ $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$ $v$

$=$

$\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$ $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$

$\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$ $u$ $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$ $v$

$+$

$\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$ $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$

.