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


where p and q are given continuous functions, can be made integrable by letting v(x) be a function such that




Then e^(v(x)) would be the integrating factor such that multiplying by y(x) gives the expression


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


See also

First-Order Ordinary Differential Equation, Ordinary Differential Equation

This entry contributed by Joakim Munkhammar

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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.

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Integrating Factor

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Munkhammar, Joakim. "Integrating Factor." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

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