Integrating Factor

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 first-order 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

			(4)
			(5)

using the product rule. Integrating both sides with respect to  then gives the solution

(6)

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: McGraw-Hill, pp. 526-529, 1953.