A general solution of a differential equation is a family that contains every solution in the class under consideration, usually through one or more arbitrary constants or functions. For example, the general real solution of is

where is the constant of integration that appears when an antiderivative is obtained in the corresponding indefinite integral. Additional initial conditions or boundary conditions select particular solutions from the family. A solution not obtained from the general family by any allowed choice of its parameters is called a singular solution.

See also

Antiderivative, Constant of Integration, Indefinite Integral, Particular Solution, Singular Solution

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References

Boyce, W. E. and DiPrima, R. C. Elementary Differential Equations and Boundary Value Problems, 9th ed. Hoboken, NJ: Wiley, 2009.

Cite this as:

Weisstein, Eric W. "General Solution." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/GeneralSolution.html

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