Given is differential equation: $2y''+5y'-3y=0$
Write this equations as 1. order system and calculate eigenvalues of the matrix of this differential equation.

My idea:

$z\_{1}=y$

$z\_{2}=y'$

$\frac{d}{dx}\begin{pmatrix} z\_{1} \\ z\_{2} \end{pmatrix} =\begin{pmatrix} z\_{2} \\ \frac{3}{2}z\_{1}-\frac{5}{2}z\_{2} \end{pmatrix} $

But how do I get matrix to calculate eigenvalues?