Definition:Homogeneous Linear Second Order ODE

Definition
A homogeneous linear second order ODE is a differential equation which is in (or can be manipulated into) the form:
 * $\dfrac {\d^2 y} {\d x^2} + \map P x \dfrac {\d y} {\d x} + \map Q x y = 0$

where, as is indicated by the notation, $\map P x$ and $\map Q x$ are functions of $x$ alone (or constants).

Also see

 * Definition:Linear Second Order ODE
 * Definition:Nonhomogeneous Linear Second Order ODE