Difference between revisions of "Order of Differential Equations"
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| − | * <math> y | + | * <math> y'' + xy' – x^3y = \sin{x} </math> is of order 2 because the highest-order derivative, <math> y'' </math>, is of order 2. |
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Revision as of 18:51, 17 September 2021
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, , is of order 2.
Resources
- Differential Equations, Lumen Learning
- []
