Inhomogeneous linear differential equation

An inhomogeneous linear differential equation has a nonzero forcing term. Its general solution is one particular solution plus the general solution of the associated homogeneous linear differential equation.

For a linear differential equation written $Ly=f$, the prescribed right-hand side $f$ is the forcing term. It may represent an external input or source, and can be constant or time dependent. Setting $f=0$ gives the associated homogeneous linear differential equation.