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📚 Differential Equations for Engineers
Chapters ▾
0 Introduction1 First order ODEs2 Higher order linear ODEs3 Systems of ODEs4 Fourier series and PDEs5 Eigenvalue problems6 The Laplace Transform7 Power series methods8 Nonlinear SystemsA Linear AlgebraB Table of Laplace Transforms

Chapter 1: First order ODEs

A first order ODE is an equation of the form

d y d x = f ( x , y )

or just

y ′ = f ( x , y )

In general, there is no simple formula or procedure one can follow to find solutions. In the next few lectures we will look at special cases where solutions are not difficult to obtain. In this section, let us assume that f is a function of x alone, that is, the equation is

y ′ = f ( x )

(1.1.1)

We could just integrate (antidifferentiate) both sides with respect to x.

Adapted from Differential Equations for Engineers by Jiří Lebl (Oklahoma State University), hosted on LibreTexts (math.libretexts.org) and licensed under CC BY-SA 4.0. Changes were made. License: CC-BY-SA-4.0.