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If the function be zi the formula of reduction is
(19) If the function be eo (cosa)" the formula of reduction is
INTEGRATION OF DIFFERENTIAL FUNCTIONS OF TWO OR MORE WARIABLES.
Sect. 1. Functions of the first order.
IN order that a differential function of two variables of the first order, such as
should be the differential of a function u, it is necessary that the condition
dP d Q
dy T do should exist. When this criterion of integrability holds good, we find
The application of these formulae may be generally facilitated by observing that in the second term of the former it is only necessary to integrate the terms in Q which involve a only, and in the latter those terms of P which involve y only.
then P = a + Q = 2 by;