Differential Equations: Basic Definitions and Terminology (Section 1.1) | Math with Professor V


Summary

The video provides an introduction to differential equations, classifying them as ordinary (ODEs) and partial (PDEs) based on the presence of ordinary or partial derivatives. It explains the concept of order in differential equations determined by the highest derivative present. Additionally, it distinguishes between linear and non-linear differential equations, focusing on first-degree derivatives and the absence of powers other than one. The video also demonstrates how to verify a solution of a differential equation by differentiating the proposed solution and substituting it back into the original equation.


Introduction to Differential Equations

Introduction to what a differential equation is and the classification based on types (ODEs and PDEs).

Classification by Type

Explaining the classification of differential equations into ordinary (ODEs) and partial (PDEs) based on the presence of ordinary derivatives or partial derivatives.

Classification by Order

Discussing the concept of order in differential equations and how to determine the order based on the highest derivative present in the equation.

Classification by Linearity

Explaining linear and non-linear differential equations based on the form of the equation, focusing on first-degree derivatives and the absence of powers other than one.

Verification of Solutions

Demonstrating how to verify a solution of a differential equation by differentiating the proposed solution and substituting it back into the original equation.

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