Embedded Files
Introduction to Differential Equations
Introduction to Differential Equations
Definition, Types of Differential Equations, Order, Degree, Linearity, Types of Solutions
SME Materials
Introduction | Carey Louise Arroyo
Topics included in this reviewer notes:
Types of Equations
Differential Equations
Types of Differential Equations
Order of Differential Equations
Degree of Differential Equations
Linear Differential Equations
Solutions of Ordinary Differential Equations
Kinds of Solutions
[1] Introduction.pdfArticles
Articles
Introduction to Differential Equations
This article introduces the reader to the topic of differential equations in a simple manner that is easy to understand. The article discusses the following differential equation topics: definition, types, order, degree, and linearity.
Basics of Differential Equations
This article contains a brief overview of the basics of differential equations. It defines what a differential equation is, explains what makes a function a solution to a DE, enumerates the types of solutions a DE may have, and illustrates how to get a particular solution of a DE when given its general solution.
Differential Equation and its Degree
This article contains a more in-depth discussion on the order and degree of a differential equation. Aside from providing the definition of a differential equation, it also thoroughly explains how to determine the order and degree of a differential equation.
Online Tutorial Videos
Online Tutorial Videos
Differentials Intro by Khan Academy
This video succinctly introduces the topic of differentials to its viewer. It defines what a differential equation and its solutions is and discusses the different notations in which a differential equation can be written as.
How to find order and degree of a differential equation by JC Amores
This video contains information on how to determine the order and degree of a differential equation. It is essentially a tutorial that uses example equations to better illustrate the topic and is appropriate for those who are having trouble differentiating between the order and degree of a differential equation.
Introduction to Differential Equations Order, Degree, Linearity (Tagalog/Filipino Math) by enginerdmath
This is a 16 minute video that includes discussions about all the topics under this section. The discussions are done by a Filipino who code-switches, so some people may find it easier to understand compared with the usual English tutorials/lectures.
Solutions of Some 1st Order Differential Equations
Solutions of Some 1st Order Differential Equations
Variable Separable, Exact DE, Linear DE, Bernoulli’s Equations, Homogenous DE
SME Materials
Solution of Some 1st Order Differential Equations I | Carey Louise Arroyo
Topics included in this reviewer notes:
Variable Separable
Exact Differential
[2] Solution of Some 1st Order Differential Equation I.pdfArticles
Articles
Variable Separable Differential Equations
This article contains comprehensive notes about variable separable differential equations. It defines what a variable separable differential equation is and gives six (6) examples with detailed solutions to solving for the general and particular solutions of the given differential equations. In the examples, the process of solving for the interval of validity is also discussed. This topic of interval of validity is not included in the Quiz 1 topics and may be disregarded for now.
Exact Differential Equations
This article discusses the topic of exact differential equations. In the article, the exact differential equation is defined and five (5) examples are given with detailed solutions to solving for the general and particular solutions of the given differential equations. In the solutions to the examples, the interval of validity is also discussed. Since the interval of validity is not included in the course syllabus for Quiz 1 topics, it may be disregarded for now.
Linear Differential Equations
This article contains notes about linear differential equations. In the article, the linear differential equation is defined and the process of solving for its general and particular solution is discussed through the use of six (6) examples. In the solutions to the examples, the interval of validity is also discussed. Since the interval of validity is not included in the course syllabus for Quiz 1 topics, it may be disregard.
Bernoulli Differential Equations
This article contains an in-depth discussion about the Bernoulli differential equations. The article defines what a Bernoulli differential equation is and presents four (4) sample problems to explain the process of solving for the general and particular solutions of Bernoulli differential equations. In the solutions to the examples, the interval of validity is also discussed. Since the interval of validity is not included in the course syllabus for Quiz 1 topics, it may be disregard.
Homogeneous Differential Equations
This article contains notes about homogeneous differential equations. It succinctly discusses the definition of a homogeneous differential equation and the process of substitution involved to solve one. It also provides four (4) sample problems with detailed solutions to explain the process of solving for the general and particular solutions of the given differential equations. In the examples, the process of solving for the interval of validity is also discussed. This topic of interval of validity is not included in the Quiz 1 topics and may be disregarded for now.
Online Tutorial Videos
Online Tutorial Videos
Separable Differential Equations (Introduction) by Houston Math Prep
This video summarizes the basics of solving separable differential equations. It defines what a separable differential equation is, explains how to identify whether or not a differential equation is separable, and demonstrates how to solve for the general solution of a separable differential equation using two (2) examples.
Separable First Order Differential Equations - Basic Introduction by The Organic Chemistry Tutor
This video contains additional examples on how to solve for the solutions to separable first order differential equations. Specifically, the process of solving for the general and particular solution of three (3) separable differential equations was shown in the video.
Exact Equations (First-Order Differential Equations) by Houston Math Prep
This video summarizes the basics of solving exact differential equations. It defines what an exact differential equation is, explains the concepts behind the exactness of a first-order differential equation, and demonstrates how to solve for the general solution of an exact differential equation using two (2) examples.
First-Order Linear Differential Equations & Integrating Factors (Introduction) by Houston Math Prep
This video summarizes the basics of solving linear differential equations. It defines what a first-order linear differential equation is, explains the concepts of integrating factors, and demonstrates how to solve for the general solution of a linear differential equation using two (2) examples.
Bernoulli First-Order Differential Equations (Introduction) by Houston Math Prep
This video summarizes the basics of solving Bernoulli’s equations. It defines what a Bernoulli’s equation is, explains how to transform a Bernoulli’s equation into a linear differential equation, and demonstrates how to solve for the general solution of a Bernoulli’s equation using an example.
Bernoulli First-Order Differential Equations (Examples) by Houston Math Prep
This video contains additional examples on how to solve for the solutions to Bernoulli’s equations. Specifically, the process of solving for the general of three (3) Bernoulli’s equations was shown in the video.
Homogeneous First-Order Differential Equations (Introduction) by Houston Math Prep
This video summarizes the basics of solving homogeneous differential equations. It defines what a homogeneous differential equation is, explains the substitution method, and demonstrates how to solve for the general solution of a homogeneous differential equation using an example.
Homogeneous First-Order Differential Equations (Examples) by Houston Math Prep
This video contains additional examples on how to solve for the solutions to homogeneous differential equations. Specifically, the process of solving for the general of three (3) homogeneous differential equations was shown in the video.
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