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# First-order differential equations

Chapter

## Abstract

This book is a study of differential equations and their applications. A differential equation is a relationship between a function of time and its derivatives. The equations
$$\frac{{dy}}{{dt}}\, = \,3{y^2}\,\sin \left( {t\, + \,y} \right)$$
(i)
and
$$\frac{{{d^3}y}}{{d{t^3}}}\, = \,e{\,^{ - y}}\, + \,t\, + \,\frac{{{d^2}y}}{{d{t^2}}}$$
(ii)
are both examples of differential equations. The order of a differential equation is the order of the highest derivative of the function y that appears in the equation. Thus (i) is a first-order differential equation and (ii) is a third-order differential equation. By a solution of a differential equation we will mean a continuous function y(t) which together with its derivatives satisfies the relationship.

## Keywords

General Solution Drag Force White Lead Separable Equation Picard Iteration
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Copyright information

© Springer-Verlag, New York Inc. 1978

## Authors and Affiliations

1. 1.Department of Mathematics Queens CollegeCity University of New YorkFlushingUSA