Ordinary differential equations | Differential equations

Homogeneous differential equation

A differential equation can be homogeneous in either of two respects. A first order differential equation is said to be homogeneous if it may be written where f and g are homogeneous functions of the same degree of x and y. In this case, the change of variable y = ux leads to an equation of the form which is easy to solve by integration of the two members. Otherwise, a differential equation is homogeneous if it is a homogeneous function of the unknown function and its derivatives. In the case of linear differential equations, this means that there are no constant terms. The solutions of any linear ordinary differential equation of any order may be deduced by integration from the solution of the homogeneous equation obtained by removing the constant term. (Wikipedia).

Video thumbnail

Determine if a First-Order Differential Equation is Homogeneous - Part 1

This video explains how to determine if a given linear first order differential equation is homogeneous using the ratio definition. Website: http://mathispower4u.com

From playlist First Order Homogeneous Differential Equations

Video thumbnail

Introduction to Homogeneous Differential Equations

Introduction to Homogeneous Differential Equations A full introduction to homogeneous differential equations.

From playlist Differential Equations

Video thumbnail

C74 Example problem

A first example problem solving a linear, second-order, homogeneous, ODE with variable coefficients around a regular singular point.

From playlist Differential Equations

Video thumbnail

C07 Homogeneous linear differential equations with constant coefficients

An explanation of the method that will be used to solve for higher-order, linear, homogeneous ODE's with constant coefficients. Using the auxiliary equation and its roots.

From playlist Differential Equations

Video thumbnail

Differential Equations | Homogeneous linear equations with constant coefficients

We introduce the strategy used for solving homogeneous linear differential equations with constant coefficients.

From playlist Linear Differential Equations

Video thumbnail

B23 Example problem solving for a homogeneous DE

The first substitution changes a DE in differential form that could not otherwise be solved (it is not exact, nor can it be changed into an exact equation by using an integrating factor) into a DE in which separation of variables can be applied. Make sure the DE is homogeneous, though.

From playlist Differential Equations

Video thumbnail

Homogeneous Differential Equations: Differential Equations Lesson #6

Some of the links below are affiliate links. As an Amazon Associate I earn from qualifying purchases. If you purchase through these links, it won't cost you any additional cash, but it will help to support my channel. Thank you! ►PRODUCT RECOMMENDATIONS https://www.amazon.com/shop/brithem

From playlist Differential Equations

Video thumbnail

Solve a First-Order Homogeneous Differential Equation in Differential Form - Part 2

This video provides an example how to to solve a homogeneous differential equation in differential form. Site: http://mathispower4u.com Search: http://mathispower4u.wordpress.com

From playlist First Order Homogeneous Differential Equations

Video thumbnail

C49 Example problem solving a system of linear DEs Part 1

Solving an example problem of a system of linear differential equations, where one of the equations is not homogeneous. It's a long problem, so this is only part 1.

From playlist Differential Equations

Video thumbnail

Prove the Form of the General Solution to a Linear Second Order Nonhomogeneous DE

This video explains the form of the general solution to linear second order nonhomogeneous differential equations. Site: http://mathispower4u.com

From playlist Linear Second Order Nonhomogeneous Differential Equations: Method of Undetermined Coefficients

Video thumbnail

Nonhomogeneous Linear Ordinary Differential Equations

In the previous video (https://youtu.be/3Kox-3APznI) we examined solving homogeneous linear ordinary differential equations (the forcing function was equal to 0). In this video we discuss how to solve nonhomogeneous linear ordinary differential equations which has the forcing function equ

From playlist Ordinary Differential Equations

Video thumbnail

Why Homogeneous Differential Equations Become Separable

If you have a DE of the form Mdx + Ndy = 0, we say it is homogeneous if both M and N are homogeneous functions of the same degree. If we let y = ux or x = vy we can then transform this DE into a separable DE. In this video I explain why this actually happens. This video does not give an ac

From playlist Homogeneous Differential Equations

Video thumbnail

MATH2018 Lecture 5.3 Non-homogeneous second-order ODEs

When an ODE has a non-zero right-hand side (the ODE is "non-homogeneous") we split the solution into two parts: the first part is simply the solution to the homogeneous equation; the second part deals with the term on right-hand side.

From playlist MATH2018 Engineering Mathematics 2D

Video thumbnail

Inhomogeneous second-order ode | Lecture 19 | Differential Equations for Engineers

How to solve an inhomogeneous, linear, second-order differential equation. Join me on Coursera: https://www.coursera.org/learn/differential-equations-engineers Lecture notes at http://www.math.ust.hk/~machas/differential-equations-for-engineers.pdf Subscribe to my channel: http://www.yo

From playlist Differential Equations for Engineers

Video thumbnail

Differential Equation - Introduction (16 of 16) 2nd Order Differential Eqn. Linear Non-Homogeneous

Visit http://ilectureonline.com for more math and science lectures! In this video I will describe 2nd order linear non-homogeneous differential equations. Firstt video in the Introduction series can be seen at: https://youtu.be/rLS4Q0KoSGI

From playlist DIFFERENTIAL EQUATIONS 1 - INTRODUCTION

Video thumbnail

Mod-03 Lec-10 First Order Linear Equations

Ordinary Differential Equations and Applications by A. K. Nandakumaran,P. S. Datti & Raju K. George,Department of Mathematics,IISc Bangalore.For more details on NPTEL visit http://nptel.ac.in.

From playlist IISc Bangalore: Ordinary Differential Equations and Applications | CosmoLearning.org Mathematics

Video thumbnail

Ex 1: Method of Undetermined Coefficients to Find the General Solution (exponential)

This video provides an example of how to find the general solution to a linear second order nonhomogeneous differential equation using the method of undetermined coefficients. Site: http://mathispower4u.com

From playlist Linear Second Order Nonhomogeneous Differential Equations: Method of Undetermined Coefficients

Video thumbnail

The method of undetermined coefficients -- differential equations 11

⭐Support the channel⭐ Patreon: https://www.patreon.com/michaelpennmath Merch: https://teespring.com/stores/michael-penn-math My amazon shop: https://www.amazon.com/shop/michaelpenn 🟢 Discord: https://discord.gg/Ta6PTGtKBm ⭐my other channels⭐ Main Channel: https://www.youtube.

From playlist Differential Equations

Video thumbnail

Differential Equations: Homogeneous DEs Introduction

Useful in their own right, homogeneous differential equations also provide a foundation for the solutions to nonhomogeneous differential equations. In this video, we explore homogeneous differential equations and possible solutions to them.

From playlist Differential Equations

Video thumbnail

(0.3.101) Exercise 0.3.101: Classifying Differential Equations

This video explains how to classify differential equations based upon their properties https://mathispower4u.com

From playlist Differential Equations: Complete Set of Course Videos

Related pages

Differential operator | Integral | Johann Bernoulli | Differential equation | Product rule | Separation of variables | Ordinary differential equation | Change of variables | Antiderivative | Homogeneous linear equation | Linear differential equation | Homogeneous function