Definition:Linear Second Order ODE with Constant Coefficients

Definition
A linear second order ODE with constant coefficients is a second order ODE which can be manipulated into the form:
 * $y'' + p y' + q y = \map R x$

where:
 * $p$ and $q$ are real constants
 * $\map R x$ is a function of $x$.

Thus it is a linear second order ODE:
 * $y'' + \map P x y' + \map Q x y = \map R x$

where $\map P x$ and $\map Q x$ are constant functions.

Also known as
The word ordering may change, for example:
 * constant coefficient linear second order ODE

Abbreviations can be used:
 * constant coefficient LSOODE

and so on.

Also presented as
Such an equation can also be presented in the form:


 * $\dfrac {\d^2 y} {\d x^2} + p \dfrac {\d y} {\d x} + q y = \map R x$

or:
 * $\paren {D^2 + p D + q} y = \map R x$