Intro To Differential Equation

Your Guide For Learning First Order Differential Equations, And Second Order Differential Equations

Created byLonzo Fulwider

Last updated 3/2025

English

What you'll learn

Learn Ordinary Differential Equation
Learn Initial Value Problems
Learn Separable Equations
Learn First Order Linear Differential Equation
Learn Solving Exact ODE
Learn Homogeneous Differential Equation
Learn Bernoulli Differential Equation
Learn Second Order Differential Equation
Learn, Real, Distinct Roots
Learn Complex Roots
Learn Wronskian
Learn Second Order Repeated Roots

Course content

1 section • 18 lectures • 15h 45m total length

Ordinary Differential Equations Part 135:16
In this video, I will introduce ordinary differential equation, and introduce the two types of differential equation, ordinary differential equation, and partial differential equation. I will explain how to determine if a differential equation is linear or nonlinear, and finally I will do examples where I verify the given function is the general solution of the ordinary differential equation.
Part 2 Of Ordinary Differential Equations27:48
This is part 2 of ordinary differential equation.
Initial Value Problems40:45
In this video, I will introduce ordinary differential equation, and introduce the two types of differential equation, ordinary differential equation, and partial differential equation. I will explain how to determine if a differential equation is linear or nonlinear, and finally I will do examples where I verify the given function is the general solution of the ordinary differential equation.
Part 2 Of Initial Value Problems27:55
This is part 2 of initial value problem. In this video, I will go more over interval of existence, and determine where a particular solution is define, continuous and differentiable.
Quiz On Ordinary Differential Equation32:53
In this video, I will do 5 question quiz on ordinary differential equation, and initial value problems.
Separable Equations58:36
In this video, we will do seven examples solving separable differential equations. We will do examples involving initial conditions, and finding the interval of validity.
First Order Linear Differential Equation1:12:42
In this video, we will go over the steps for solving linear differential equation, we will do five examples.
Soving Exact ODE1:12:37
In this video, I will do eight examples solving exact differential equations.
Homogeneous Differential Equation1:25:20
In this video, we will do five examples solving homogeneous differential equations.
Bernoulli Differential Equation44:33
In this video, we will do three examples solving Bernoulli differential equations with the correct substitutions.
Second Order Differential Equation Real, Distinct Roots41:21
In this video, we will go over all the steps for finding second order differential equation real, distinct roots.
Complex Roots52:03
In this video, we will do five examples of solving second order differential equation, complex roots. We will go over principle of superpostion, two forms of the general form, and go over transient terms and solutions.
Wronskian42:14
In this video, we are going fundamental sets of solution, how will we know if we get a solution to our differential equation? We will go over linearly independent and dependent, the Wronskian and its properties which will help us solve homogeneous and non homogeneous secod and higher order differential equations. Finally, we will go over Abel's theorem which is an alternate method of computing Wronskian.
Second Order Repeated Roots1:15:38
In this video, we will go over how to solve homogeneous linear and higher order differential equations with constant coefficients that have repeated roots.
Second Order Differential Equation Undetermined Coefficients1:09:34
In this video, we will go over how to find a solution of a higher order nonhomogeneous linear differential equations with constant coefficients also known as undetermined coefficients.
Second Order Differential Equations: Differential Operators1:14:54
Second Order Differential Equation: Cauchy Euler Equation24:14
Second Order Differential Equations: Variation Of Parameters1:06:55

Requirements

Calculus 2

Description

This is a lower-level introduction to differential equation course. This course is broken into 6 sections:

1) Intro to differential equations, 2) First order differential equations, 3) Second order differential equations, 4) Series solution, 5) Laplace transform. First, we will go over definitions and terminology, we will go over the difference between linear non linear equations. Then storm into initial value problems, go over the difference between first order DE, second order DE, ordinary differential equations, classify ODE by order and linearity.

The first thing we will go over is define a differential equation. A differential equation is an equation containing the derivatives of one or more dependent variables with respect to one or more independent variables(equation involving some unknown function and one or more of its derivatives). In a differential equation the solution is always going to be an equation. There are two types of differential equations: ordinary differential equation, partial differential equation. Also a differential equation can be linear or nonlinear.

First Order Differential Equations:

Direction fields
Separable equations
Euler's method
First order linear differential equation
Solving exact ODE's
Homogeneous Differential Equation
Bernoulli differential equation
Linear and nonlinear models
Predator prey models and electrical newtworks

Second Order Differential Equations

Distinct real roots
Complex roots
Repeated roots
Wronskian
Undetermined coefficients
Differential operators
Variation of parameters
Cauchy euler equation
Mechanical vibrations

Series Solutions

Power series
Series Solutions

Laplace Transform

Laplace transform overview
Inverse laplace transforms
Initial value problems with laplace transforms
Translation theorems of laplace transforms

Systems Of Differential Equations

Homogeneous linear systems
Phase plane portraits

Who this course is for:

Pre Med Major, All Engineer Major, And Math Major