I'd like to know if a 2nd order of ODE of system linear has this format:

$\displaystyle \begin{matrix} a_{11} \frac{\partial^2 x}{\partial u^2} + a_{12} \frac{\partial^2 y}{\partial u^2} + b_{11} \frac{\partial x}{\partial u} + b_{12} \frac{\partial y}{\partial u} + c_{11} x + c_{12} y = 0 \\ a_{21} \frac{\partial^2 x}{\partial u^2} + a_{22} \frac{\partial^2 y}{\partial u^2} + b_{21} \frac{\partial x}{\partial u} + b_{22} \frac{\partial y}{\partial u} + c_{21} x + c_{22} y = 0 \\ \end{matrix}$

In other words, when you think about a "2nd order of ODE of system linear", do you think in a system like this above?