Definition:Homogeneous Linear Second Order ODE with Constant Coefficients

Definition
A constant coefficient homogeneous linear second order ODE is a second order ODE which can be manipulated into the form:
 * $y'' + p y' + q y = 0$

where $p$ and $q$ are real constants.

Thus it is a homogeneous linear second order ODE:
 * $y'' + P \left({x}\right) y' + Q \left({x}\right) y = 0$

where $P \left({x}\right)$ and $Q \left({x}\right)$ are constant functions.