The order of the ODE refers to the order of the derivative on the left-hand side in the equation $$\begin{equation} \frac{dy}{dt}=f(t,y). \tag{1} \end{equation}$$ This equation is of first order and $f$ is an arbitrary function. A second-order equation goes typically like $$\begin{equation} \frac{d^2y}{dt^2}=f(t,\frac{dy}{dt},y). \tag{2} \end{equation}$$ A well-known second-order equation is Newton's second law $$\begin{equation} m\frac{d^2x}{dt^2}=-kx, \tag{3} \end{equation}$$ where $k$ is the force constant. ODE depend only on one variable