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

• Results about homogeneous linear second order ODEs can be found here.

Sources

• 1972: George F. Simmons: Differential Equations ... (previous) ... (next): $\S 3.14$: Second Order Linear Equations: Introduction