According to Ince, *Ordinary Differential Equations*, Art. 2.13 (fn):
"The application of the method [of variations of parameters] to the linear
equation of the first order is due to John Bernoulli, *Acta Erud.,* 1697,
but the solution by quadratures was known to Leibniz several years later."
And ibid., Art. 5.23 Ince attributes the application of the method to
general non-homogeneous DEs to Lagrange, *Nouv. M\'em. Acad. Berlin*, 5
(1774), 6 (1775).
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