# Integrating Factor

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## integrating factor

[′int·ə‚grād·iŋ ′fak·tər]
(mathematics)
A factor which when multiplied into a differential equation makes the portion involving derivatives an exact differential.

## Integrating Factor

a factor multiplication by which transforms the left-hand side of the differential equation

(*) P(x, y) dx + Q(x, y) dy = 0

into the total differential of some function U(x,y). Thus, if μ(x,y) is an integrating factor, then

μ(x, y)[P(x, y) dx + Q(x, y) dy] = dU(x, y)

If the factor μ(x,y) is known, then the problem of integrating the original equation (*) reduces to quadratures, since it remains to find the function U(x,y) from its total differential.

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