Consider the initial value problem

$$\left\lbrack \begin{array}{c} y_1^{\,\prime} \\ y_2^{\,\prime} \end{array} \right\rbrack = \left\lbrack \begin{array}{rr} 0 & 1 \\ -4 & -5 \end{array} \right\rbrack \left\lbrack \begin{array}{c} y_1 \\ y_2 \end{array} \right\rbrack + \left\lbrack \begin{array}{c} 0 \\ 5\cos\!\left(4t\right) \end{array} \right\rbrack,$$

$$\left\lbrack \begin{array}{c} y_1(-3) \\ y_2(-3) \end{array} \right\rbrack = \left\lbrack \begin{array}{r} 2 \\ -1 \end{array} \right\rbrack.$$
This initial value problem was obtained from an initial value problem for a higher order scalar differential equation, via the change of variables $y_1 = y$ and $y_2 = y'$. What is the corresponding scalar initial value problem?

1. Differential equation: help (equations)
   
   (Give your answer in terms of $y, y^{\,\prime}, y^{\,\prime\prime}, t$. )
   
   
2. Initial conditions: and help (equations)
   
   (Give your first answer in the form $y(t_0) = y_0$. Give your second answer in the form $y'(t_0) = y_0'$. )