12 Facts About Differential equations

Differential equations first came into existence with the invention of calculus by Newton and Leibniz.

Differential equations solves these examples and others using infinite series and discusses the non-uniqueness of solutions.

An example of modeling a real-world problem using differential equations is the determination of the velocity of a ball falling through the air, considering only gravity and air resistance.

Apart from describing the properties of the equation itself, these classes of differential equations can help inform the choice of approach to a solution.

Linear differential equations are the differential equations that are linear in the unknown function and its derivatives.

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Linear differential equations frequently appear as approximations to nonlinear equations.

Differential equations are described by their order, determined by the term with the highest derivatives.

Differential equations that describe natural phenomena almost always have only first and second order derivatives in them, but there are some exceptions, such as the thin film equation, which is a fourth order partial differential equation.

Theory of differential equations is closely related to the theory of difference equations, in which the coordinates assume only discrete values, and the relationship involves values of the unknown function or functions and values at nearby coordinates.

Study of differential equations is a wide field in pure and applied mathematics, physics, and engineering.

The mathematical theory of differential equations first developed together with the sciences where the equations had originated and where the results found application.

Whenever this happens, mathematical theory behind the Differential equations can be viewed as a unifying principle behind diverse phenomena.