Step By Step Calculus » 16.0 - History and Applications

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History and Applications
Note that every indefinite integration problem is actually an example of a simple differential equation, thus the indefinite integrals can be considered to be subsumed in differential equations.
“Differential equations” began with Leibniz, the Bernoulli brothers and others from the 1680’s, not long after Newton’s ‘fluxional equations’ in the 1670’s. They applied differential equations largely to geometry and mechanics. In 1755, Euler proposed the first method of integrating linear ordinary differential equations with constant coefficients.
One can find applications of differential equations in engineering, business, and even in biology. Newton’s law of cooling, electrical circuits are the common examples where we see differential equations. In biotechnology, many biological processes are modelled using differential equations.