Definition:Reduced Equation of Linear ODE with Constant Coefficients

Definition
Consider the linear $n$th order ODE with constant coefficients:
 * $(1): \quad \ds \sum_{k \mathop = 0}^n a_k \dfrac {\d^k y} {d x^k} = \map R x$

The equation:
 * $\ds \sum_{k \mathop = 0}^n a_k \dfrac {\d^k y} {d x^k} = 0$

is the reduced equation of $(1)$.