In mathematics, history of differential equations traces the development of "differential equations" from calculus, itself independently invented by English physicist Isaac Newton and German mathematician Gottfried Leibniz.

How differential equations are formed?

In general, the differential equation of a given equation involving n parameters can be obtained by differentiating the equation successively n times and then eliminating the n parameters from the (n+1) equations.

Why was the differential equation invented?

In biology and economics, differential equations are used to model the behavior of complex systems. The mathematical theory of differential equations first developed together with the sciences where the equations had originated and where the results found application.