A linear dynamic system is one that can be described by a set of linear, ordinary differential

equations of the following type:

$\frac{du}{dt}=Au$

Given

$A=\left[\begin{array}{cc}2& -4\\ 3& -2\end{array}\right]$

along with the initial condition

$u(0)=\left[\begin{array}{c}1\\ 1\end{array}\right]$

Use MATLAB to find the complete solution

$u(t)=c_1{x}_1{e}^{{}_{1}t}+c_2{x}_2{e}^{{}_{2}t}$

including the constants $c_1$ and $c_2.$

Plot the solutions $u(t)$ for a long enough time to show their behavior.