This is certainly relevant for modern science, but seldom is the history of the ideas and organic development taught for some scientific subjects. This short article is gramatically poor, but rich in content.
This decent little video explains basically what differential equations are, as some background for the subject in general.
This article is a bit better written than the one I posted above and focuses more on the early history of differential equations. Leibniz, Newton, (Jacob or James) Bernoulli, and Johann Bernoulli are arguable progenitors of the subject. It's about eight pages.
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