Differential Equations for EngineersXYZ Homework Edition

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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 y1y_1, y2y_2,..., yny_n, then we can have a differential equation involving all of them and their derivatives. For example, y1″=f(y1′,y2′,y1,y2,x)y''_1= f(y'_1,y'_2,y_1,y_2,x). Usually, when we have two dependent variables we have two equations such as

Adapted from Differential Equations for Engineers by Jiří Lebl (https://www.jirka.org/diffyqs/), © Jiří Lebl, licensed under CC BY-SA 4.0. Changes were made. License: CC-BY-SA-4.0.

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