Let $x(t)=$

$\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$ $x_1(t)$ $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$ $x_2(t)$

be a solution to the system of differential equations:

$\begin{array}{rrrrrr}x^\prime_1(t)&=&& 3 \,x_1(t)&+& 2 \, x_2(t)\\x^\prime_2(t)&=&& -4 \, x_1(t)&- &3 \,x_2(t)\\ \end{array}$

If $x(0)=$

$\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$ -3 $\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$ 2

, find $x(t)$.

Put the eigenvalues in ascending order when you enter $x_1(t), x_2(t)$ below.

$x_{1}(t)=$ $\exp($ $t)+$ $\exp($ $t)$

$x_{2}(t)=$ $\exp($ $t)+$ $\exp($ $t)$