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:

• $y''+xy'-x^{3}y=\sin {x}$ is second order because the highest-order derivative, $y''$, is of order 2.
• $x't+x=t^{2}$ is first order because x' is the highest order derivative.
• $y'''+3y''+3y'+y=x^{2}$ is of order 3.

Resources

• Differential Equations, Lumen Learning
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