# Simultaneous Differential Equation And Its Application

Simultaneous Differential Equation And Its Application

## Chapter One

### 1.0 Introduction

In mathematics, the history of differential equation traces the development of â€śD.Eâ€ť from calculus, with itself was independently inverted by English physicist Isaac Newton and German mathematician Gottfried Lebnize.

Sir Isaac Newton (1642-1727) and Goltfied wihelm Leibniz (1646-1716) were the two prominent scientists who independently discovered the fundamental ideas of calculus. This provides a tool for solving problems involving motion and other physical phenomena such as elacticity, analysis of the bending of beams and the shape a string will form under various conditions.

Generally, first-order and higher-order differential equations problems analytically.

Langrange said of Eulerâ€™s work in mechanics identified the condition for exactness of first order differential equation in (1734-1735) developed the theory of integrating factors and gave the general solution of homogeneous.

The brothers jakob (1654-1705) and johann (1667-1748) bernailli of basel did much to develop methods of solving differential equations, with the aid of calculus they formulated as differential equations and solved a number of problems in mechanics. In the same paper (in 1690) he firt used the term â€śintegralâ€ť in the modern sense. In 1694 johann Bernoulli was able to solve the equation

Even though it was not yet known that d (In x) =

Which led to much friction between them, was the brachristochrone problem. The determination of the curve of fastest decent.

The brachistrochone was also solved by Leibniz and newton in addition to Bernoulli brother.

The study of differential equation originated in the beginnings of the calculus. Newton did relatively work in differential equations, his development of the calculus and elucidation of the basic principles of mechanics provided a basis for their application in the eighteenth century, most notably by Euler. Newton classified first order differential equation which is written in the form = f(x)

= f (y) and = f(x,y)

By the end of the eighteenth century many elementary methods of solving ordinary differential equations had been discovered. In the nineteenth century interest turned toward the investigation of the theoretical equations of existence and uniqueness and to the development of less elementary methods such as those based on power series method. Partial differential equations also began to be studied intensively, as their crucial role in mathematical physics became clear.

In 1693, Leibniz solved his first differential equation and that same year newton published the results of previous D.E solution methods a year that is said to mark the inception for D.E as a distinct field in mathematics.

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## Simultaneous Differential Equation And Its Application

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