Differential Equations: Definitions and Terminology (Level 3 of 4)

The video tutorial explains how to classify Ordinary Differential Equations (ODEs) by order and linearity. It provides examples of different ODEs, demonstrating how to identify the dependent and independent variables, determine the order by identifying the highest derivative, and assess linearity by checking if the dependent variable and its derivatives are linear and expressed in terms of the independent variable. The video covers examples of third-order linear, second-order linear, second-order nonlinear, first-order nonlinear, and second-order linear ODEs.

What is the first step in classifying a differential equation?

How can the given differential equation be rewritten using Leibniz notation?

What is the order of the first example ODE discussed?

What conditions must be met for an ODE to be classified as linear?

What are the three requirements for classifying an ODE as linear?

In the second example, what is the highest derivative present?

What makes the third example ODE nonlinear?

What is the significance of constants in the context of the ODEs discussed?

How is the fourth example ODE classified in terms of order and linearity?

What is the final classification of the last example ODE?