An integrating factor is a function by which an ordinary differential equation can be multiplied in order to make it integrable. For example,
a linear firstorder ordinary
differential equation of type

(1)

where
and
are given continuous functions, can be made
integrable by letting be a function such that

(2)

and

(3)

Then
would be the integrating factor such that multiplying by gives the expression
using the product rule. Integrating both sides with respect to
then gives the solution

(6)

See also
FirstOrder Ordinary Differential Equation,
Ordinary
Differential Equation
This entry contributed by Joakim
Munkhammar
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References
Adams, R. A. Calculus: A Complete Course, 4th ed. Reading, MA: Addison Wesley, 1999.Morse,
P. M. and Feshbach, H. Methods
of Theoretical Physics, Part I. New York: McGrawHill, pp. 526529,
1953.Referenced on WolframAlpha
Integrating Factor
Cite this as:
Munkhammar, Joakim. "Integrating Factor." From MathWorldA Wolfram Web Resource, created by Eric
W. Weisstein. https://mathworld.wolfram.com/IntegratingFactor.html
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