Forcing function (differential equations)

In a system of <a href="/facts/Differential_equations/9MGbE3Ca">differential equations</a> 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
 )
 
 
 {\displaystyle f(t)}
 
 is the forcing function in the nonhomogeneous, second-order, ordinary differential equation:

a
        
          y
          ″
        
        +
        b
        
          y
          ′
        
        +
        c
        y
        =
        f
        (
        t
        )
      
    
    {\displaystyle ay''+by'+cy=f(t)}

Forcing function (differential equations) open-in-new

Forcing function (differential equations)