Science:Math Exam Resources/Courses/MATH152/April 2012/Question 08 (c)/Statement

Consider the 2 x 2 system of differential equations

${\mathbf{𝐱}}^{\prime }(t)=\left[\begin{array}{cc}-1& -2\\ 2& -1\end{array}\right]\mathbf{𝐱}(t)$

where $\mathbf{𝐱}(t)=\left[\begin{array}{c}{x}_1(t)\\ x_2(t)\end{array}\right]$ is the vector of unknown functions.

Based on the results in (a) and (b), write down the general solution in real-valued form.