Order of Differential Equations

Introduction

The order of a differential equation is determined by the highest-order derivative. The higher the order of the differential equation, the more arbitrary constants need to be added to the general solution. A first-order equation will have one, a second-order two, and so on. The degree of a differential equation, similarly, is determined by the highest exponent on any variables involved.

Examples:

• Failed to parse (syntax error): {\displaystyle y" + xy' – x^3y = sin x } is of order 2 because the highest-order derivative, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y" } , is of order 2.

Resources

• Differential Equations, Lumen Learning
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