Constant-coefficient differential equation ($a_n{y}^{(n)}+\cdots +a_1{y}^{\prime }+a_{0}y=f(x)$)

A linear ordinary differential equation has constant coefficients when the multipliers $a_j$ of the unknown function and its derivatives do not depend on the independent variable. The forcing $f$ may still vary. For the homogeneous equation $f=0$, its characteristic equation of a constant-coefficient differential equation determines exponential solutions.