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This paper deals with the study of first-order ordinary differential equations with constant coefficients and their applications. Some main types of such equations have been discussed. The areas of application of these equation were survey, in particular, application to mechanics (the flight of a projectile motion) which when take “up” and “right” as the positive directions; by newton’s second law of motion (Fx =Max or Fy = May): the motion of plannet in our solar system; by astronomy which interesting to make use of the law of gravitational force to describe the movement of planets in the solar system. The study of this equation is important because it is one of the types of equation used in solving real-life problems especially in science and engineering.
1.0 Introduction
In mathematics, the history of differential equation traces the development of “D.E” 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 Euler’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 “integral” in the modern sense. In 1694 johann Bernoulli was able to solve the equation
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