Definition:Second Order Ordinary Differential Equation

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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:

$\ds \map F {x, y, \frac {\d y} {\d x}, \frac {\d^2 y} {\d x^2} }$

or, using prime notation:

$\map F {x, y, y^\prime, y^{\prime \prime} }$

Historical Note

Much of the theory of Second Order ODEs was progressed by Leonhard Paul Euler.