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Method of integrating factor: could be applied to first order equation $M(x,y)dx+N(x,y)dy=0$ which we multiply by $\mu$ to make it exact.

Method of variation of parameters could be applied to linear inhomogeneous first and higher order equations. See sections 2.1 and 3.6 (and later 4.4 and 7.9). For homogeneous equation solution is $y=C_1y_1+C_2y_2+\ldots+C_n y_n$ with constants $C_1,\ldots, C_n$ and for inhomogeneous equation solution is searched in the form $y=C_1y_1+C_2y_2+\ldots+C_n y_n$ with unknown functions $C_1,\ldots, C_n$.

For first order linear equations these methods are equivalent.