 # Differential Equations PDF

A differential equation can simply be termed as an equation with one or more functions and its derivatives. You can read more about it from the differential equations PDF below. The functions usually represent physical quantities, and derivatives of these functions give the rate of change of the quantities, and the differential equation describes the relationship between them. The simplest way to calculate quantities is by using differential equations formulas.

### PDF of Differential Equations

Mathematically, we can define the differential equation as given below:

For a given function g, find a function f such that

dy/dx = g(x), where y = f(x)

This form of the equation is known as a differential equation. Differential Equations are used to solve practical problems like Elmer Pump Heat Equation.

History:

Differential Equations first came into existence by Newton and Leibniz, who also invented Calculus. The three kinds of equations Newton initially conceptualized were: The study of differential equations essentially consists of the sequence of their solutions. That means the set of functions that satisfy each of the equations and the attributes of their solutions. Explicit formulas are used for solving only the simplest differential equations; but, many properties of solutions of a given differential equation may be determined without even estimating them accurately.

Applications:

Differential equations have a wide range of applications in Physics, Chemistry, Biology and even Economics, with topics ranging from classical mechanics, electrodynamics, general relativity and quantum mechanics. Therefore, in-depth knowledge of differential equations has found principal importance in all the latest scientific researches.