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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 3: Systems of ODEs

Often we do not have just one dependent variable and just one differential equation, we may end up with systems of several equations and several dependent variables even if we start with a single equation.

If we have several dependent variables, suppose y1, y2,..., yn, then we can have a differential equation involving all of them and their derivatives. For example, y1″=f(y1′,y2′,y1,y2,x). Usually, when we have two dependent variables we have two equations such as

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.