Definition:Second Order Ordinary Differential Equation

Definition
A second order ordinary differential equation is an ordinary differential equation in which any derivatives with respect to the independent variable have order no greater than $2$.

The general second order ODE can be written as:
 * $\displaystyle F \left({x, y, \frac {\mathrm d y} {\mathrm d x}, \frac {\mathrm d^2 y} {\mathrm d x^2}}\right)$

or, using prime notation:
 * $F \left({x, y, y^{\prime}, y^{\prime \prime}}\right)$