Differential Equations: Classification

Differential equations exhibit fascinating variation, with a division as diverse as regular, algebraic equations. Possessing knowledge about the various types and correctly applying that knowledge to identify a particular one is a key step in solving any differential equation. This is because, it gives an idea/hint about which method can be used in that particular scenario, saving time and energy. While the classification can get very complex, most of the basic, yet crucial, differences are highlighted here.

TYPES OF DIFFERENTIAL EQUATIONS

The classifications for all differential equations include:  

Ordinary differential equations [ODE] (1 or more functions of the same independent variables and its derivatives) V/S Partial differential equations [PDE] (functions of different independent variables and its derivatives). 

                                       

Linear differential equations (a function and its derivatives as unique terms and not multiplied/raised to power/part of trigonometric or exponential functions) V/S Non-linear differential equations (functions or its derivatives could be multiplied/raised to power/part of trigonometric or exponential functions).

Order of differential equations (denotes the highest order of derivative present in the equation) [further discussed in the previous post] and Degree of differential equations (denotes the highest power of any derivative in the equation).

                                                                                      

Identifying these properties of a differential equation is truly central in the process of its simplification, since there are specific methods for specific cases. Sometimes, this early identification may reveal a far simpler method and, equally importantly, sometimes it may warn us if a differential equation is unsolvable. Learn more about the ways to solve a differential equation, and about the topic in its entirety, through this oversimplified presentation.