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

Consider the system of differential equations

$$\begin{array}{rcl} y_1^{\,\prime} & = & y_1 - 2 y_2, \\ y_2^{\,\prime} & = & y_1 + 4 y_2, \end{array}$$
with solutions

$$\begin{array}{rcl} y_1(t) & = & 2c_{1}e^{2t}+c_{2}e^{3t}, \\ y_2(t) & = & -c_{1}e^{2t}-c_{2}e^{3t}, \end{array}$$
for any constants $c_1$ and $c_2$. Rewrite the solution of the equations in vector form as $\boldsymbol{\vec{y}}(t) = c_1 \boldsymbol{\vec{y}_1}(t) + c_2 \boldsymbol{\vec{y}_2}(t)$.