Forcing function (differential equations)

In a system of differential equations used to describe a time-dependent process, a forcing function is a function that appears in the equations and is only a function of time, and not of any of the other variables. In effect, it is a constant for each value of ''t''.

In the more general case, any nonhomogeneous source function in any variable can be described as a forcing function, and the resulting solution can often be determined using a superposition of linear combinations of the homogeneous solutions and the forcing term.

For example, $f(t)$ is the forcing function in the nonhomogeneous, second-order, ordinary differential equation:
$ay'' + by' + cy = f(t)$

References

Differential equations

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