$(1$ point$)$ Consider the second order differential equation with initial conditions

$u^{\text{'}\text{'}}-4\mathrm{.}5u^{\text{'}}-6u=8sin(3t),u(1)=1,u^{\text{'}}(1)=2\mathrm{.}5.$

Without solving $it,$ rewrite the differential equation $asan$ equivalent set $of$ first order equations. $In$ your answer use the single letter $uto$ represent the function $u$ and

the single letter $vto$ represent the "velocity function" $u^{\text{'}}.Do$ not use $u(t)orv(t)to$ represent these functions. Expressions like $sin(t)$ that represent other functions

are $OK.$

$u^{\text{'}}=$

$v^{\text{'}}=$

Now write the first order system using matrices:

$\frac{d}{dt}\left[\begin{array}{c}u\\ v\end{array}\right]=\left[\begin{array}{c}\\ \end{array}\right]$

The initial value $of$ the vector valued solution for this system $is$: