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Find the most general real-valued solution to the linear system of differential equations $\displaystyle \boldsymbol{\vec{x}^{\, \prime}} = \left\lbrack \begin{array}{rr} 1 & -2 \\ 2 & 5 \end{array} \right\rbrack \boldsymbol{\vec{x}}.$

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

$= c_1$

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

$+ \ c_2$

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