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Nonhomogeneous Differential Equation

A nonhomogeneous differential equation in the linear setting is a differential equation of the form

L[y]=f

in which L is a linear operator on functions and the forcing term f is not identically zero. The associated homogeneous differential equation is L[y]=0.

If y_p is one particular solution of the nonhomogeneous equation and y_h is an arbitrary solution of the associated homogeneous differential equation, then every solution of the nonhomogeneous equation has the form

y=y_p+y_h.

Methods for finding y_p include variation of parameters and the undetermined coefficients method.

See also

Homogeneous Ordinary Differential Equation, Linear Operator, Linear Partial Differential Equation, Particular Solution, Variation of Parameters

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References

Boyce, W. E. and DiPrima, R. C. Elementary Differential Equations and Boundary Value Problems, 7th ed. New York: Wiley, 2001.

Cite this as:

Weisstein, Eric W. "Nonhomogeneous Differential Equation." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/NonhomogeneousDifferentialEquation.html

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