I have system of equations
\begin{equation} \begin{cases} \frac{dx}{dt} = x\\ \frac{dy}{dt} = y \end{cases}\, \end{equation}
It's easy to see that \begin{equation} \begin{cases} x = c_1e^t\\ y = c_2e^t \end{cases}\, \end{equation}
is a solution.
But they ask me, to show that any second order equation obtained from the system in is not equivalent to this system, in the sense that it has solutions that are not part of any solution of the system. That way it will be shown that higher order equations are equivalent to systems, the reverse is not true, and systems are more general.
I have no idea how to obtain second order equation from this system. If $\frac{dx}{dt}$ would depend on $y$ then I could do something.