Integrating Factor

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.

单词	integrating factor
释义	Integrating Factor 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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