Definition:Linear Second Order Ordinary Differential Equation

Definition
A linear second order ordinary differential equation is a differential equation which is in (or can be manipulated into) the form:
 * $\dfrac {\mathrm d^2 y} {\mathrm d x^2} + P \left({x}\right) \dfrac {\mathrm d y} {\mathrm d x} + Q \left({x}\right) y = r \left({x}\right)$

Also presented as
A linear second order ordinary differential equation can also be presented as:
 * $\dfrac {\mathrm d^2 y} {\mathrm d x^2} = P \left({x}\right) \dfrac {\mathrm d y} {\mathrm d x} + Q \left({x}\right) y + r \left({x}\right)$