This is the second part of a three-part problem.

Consider the system of differential equations

$$\begin{array}{rcl} y_1^{\,\prime} & = & y_1 - 2 y_2, \\ y_2^{\,\prime} & = & y_1 + 4 y_2. \end{array}$$
Verify that for any constants $c_1$ and $c_2$, the functions

$$\begin{array}{rcl} y_1(t) & = & 2c_{1}e^{2t}+c_{2}e^{3t}, \\ y_2(t) & = & -c_{1}e^{2t}-c_{2}e^{3t}, \end{array}$$
satisfy the system of differential equations. Enter $c_1$ as c1 and $c_2$ as c2.

1. Find the value of each term in the equation $y_1^{\,\prime} = y_1 - 2 y_2$ in terms of the variable $t$. (Enter the terms in the order given.)
   
   = + .
   
   
2. Find the value of each term in the equation $y_2^{\,\prime} = y_1 + 4 y_2$ in terms of the variable $t$. (Enter the terms in the order given.)
   
   = + .