Differential Equations with the Math Sorcerer

Name: Differential Equations with the Math Sorcerer
Rating: 4.8 (691 reviews)

Complete Differential Equations Course with TONS of worked problems and assignments:)

Created byThe Math Sorcerer

Last updated 5/2026

English

What you'll learn

Determining the Type and Order of a Differential Equation
Determining whether a Differential Equation is Linear or Nonlinear
Understand the Different Types of Solutions of Differential Equations: one-parameter families, two-parameter families, singular solutions, general solutions
Understand Initial Value Problems and the Interval of Definition
How to Solve Separable Differential Equations, First Order Linear, Exact, Homogeneous, Bernoulli, and DE's of the form dy/dx = f(Ax + By + C)
How to Determine if Functions are Linearly Independent or Dependent using the Definition
How to Prove Functions are Linearly Independent using the Wronskian
How to Solve Higher Order Linear Homogeneous Differential Equations with Constant Coefficients
How to Solve DE's with the Method of Undetermined Coefficients(The Superposition Principle)
How to Solve DE's with Variation of Parameters
How to Solve Cauchy-Euler Differential Equations
How to Compute Laplace Transforms with the Definition
How to Compute Laplace Transforms and Inverse Laplace Transforms with Tables, Partial Fractions, and Trigonometric Identities
How to use the First Translation Theorem to Compute Laplace Transforms
How to use the Derivatives of Transforms Theorems
How to Solve DE's using Laplace Transforms
Understand what the Unit Step Function is and use it to Find the Laplace Transform of a Piecewise Function
Understand what the Dirac Delta Function is
How to use the Second Translation Theorem to compute Laplace Transforms and Inverse Laplace Transforms
How to Solve DE's that involve the Dirac Delta Function
How to Find the Minimum Radius of Convergence
How to Solve DE's using Power Series

Course content

27 sections • 167 lectures • 11h 33m total length

Introduction to Differential Equations4:08
- Explain what a differential equation is.
- Determine the type of differential equation.
- Determine the order of a differential equation.
Linear Versus Nonlinear Differential Equations7:17
- Determine the difference between linear and nonlinear differential equations.
- You should be able to complete the assignment after watching this video.
- This is a very hard concept for people to learn, I hope this video helps:)
Assignment 1 with Solutions0:03
Download the file and complete the worksheet.
Solutions are included on the second page.
More Examples of Linear versus Nonlinear Differential Equations1:52
This video has full solutions to the worksheet above.
Make sure to try the worksheet before watching this video:)
Solutions to Differential Equations10:52
This is a "super video". It covers so many beautiful concepts. See the list of topics below.
- one parameter family of solutions
- two parameter family of solutions
- particular solution
- explicit solutions
- implicit solutions
- show a function is a solution
- interval of definition
- singular solutions
- trivial solution
Initial Value Problems4:52
This video explains the notion of an initial value problem. Later in the course we will solve many of these together.
An Initial Value Problem and Finding the Interval of Definition: Key Example!8:04
This is a priceless example of something that comes up in every single differential equations course. It's worth watching and learning the process.
Assignment 2 with Solutions0:03
Download the file and complete the worksheet.
Solutions are included on the second page.

Introduction to Separable Differential Equations6:24
How to Solve a Separable Differential Equation: Example 12:55
This is a good first example that explains the steps.
This example also discusses the two ways to write your solution, explicit versus implicit.
How to Solve a Separable Differential Equation: Example 21:55
This is an easier example but an important one.
The technique used here comes up over and over again.
How to Solve a Separable Differential Equation: Example 36:22
How to Solve a Separable Differential Equation: Example 42:16
How to Solve a Separable Differential Equation: Example 54:55
Separable Differential Equation Initial Value Problem: Example 13:07
Separable Differential Equation Initial Value Problem: Example 24:09
Assignment 3 with Solutions0:03
Download the file and complete the worksheet.
Solutions are included on the second page.

Introduction to Linear Differential Equations9:37
How to Solve a First Order Linear Differential Equation: Example 17:04
How to Solve a First Order Linear Differential Equation: Example 22:49
How to Solve a First Order Linear Differential Equation: Example 35:17
How to Solve a First Order Linear Differential Equation: Example 48:37
Assignment 4 with Solutions0:03
Download the file and complete the worksheet.
Solutions are included on the second page.

Introduction to Exact Differential Equations19:17
Determine if the Differential Equation is Exact: Example 10:59
Determine if the Differential Equation is Exact: Example 21:09
Determine if the Differential Equation is Exact: Example 31:50
How to Solve an Exact Differential Equation Example 14:08
How to Solve an Exact Differential Equation Example 27:06
How to Solve an Exact Differential Equation Example 34:43
Assignment 5 with Solutions0:03
Download the file and complete the worksheet.
Solutions are included on the second page.

Are the Functions Linearly Independent or Dependent? Use the definition. EX 14:28
Are the Functions Linearly Independent or Dependent? Use the definition. EX 23:20
Linearly Independent Functions with Zero Wronskian: The First Example(1889)5:26
How to Prove Functions are Linearly Independent using the Wronskian3:29
Assignment 9 with Solutions0:03
Download the file and complete the worksheet.
Solutions are included on the second page.

Introduction to Higher Order Linear Differential Equations11:25
Homogeneous Linear DE Example 12:00
Homogeneous Linear DE Example 21:41
Homogeneous Linear DE Example 33:12
Homogeneous Linear DE Example 43:41
Homogeneous Linear DE Example 51:27
Homogeneous Linear DE Example 61:02
Homogeneous Linear DE Example 71:44
Homogeneous Linear DE Example 84:42
Homogeneous Linear DE Example 92:12
Homogeneous Linear DE Example 103:24
Homogeneous Linear DE Example 115:10
Homogeneous Linear DE Example 124:20
Assignment 10 with Solutions0:03
Download the file and complete the worksheet.
Solutions are included on the second page.

Requirements

You should know basic calculus.
The ability to integrate well helps, but all integration techniques are reviewed in the problems.

Description

This is a complete college level course in Differential Equations with TONS of examples.

*** In order to get the most out of the course you should know Calculus ***

Basically just,

1) Watch the videos, and try to follow along. Try to do the problems before I do them if you can. If you can't, no big deal:)

2) After each section there is short assignment(with solutions).

3) Repeat!

If you finish even 50% of this course you will know A LOT of Differential Equations and more importantly just a lot of really solid mathematics.

Differential Equations is an awesome class not just because of the differential equations but because of all of the other key math techniques you learn in the process. This course covers all the key techniques usually covered in most differential equations courses. After taking this course you should know a lot of differential equations and roughly the equivalent of what is taught in a college level course. The hardest thing about this course is the integration techniques, most of which are learned in Calculus 1 and Calculus 2. I have tried to explain these techniques when they come up so hopefully you can follow along and learn lots of math.

I hope you enjoy watching these videos and working through these problems as much as I have:)

Who this course is for:

Students who want to learn Differential Equations.
Students who plan to take Differential Equations.
Students currently taking Differential Equations.

Differential Equations with the Math Sorcerer

What you'll learn

Explore related topics

Course content

Introduction to the Course8 lectures • 37min

Separable Differential Equations9 lectures • 32min

First Order Linear Differential Equations6 lectures • 33min

Exact Differential Equations8 lectures • 39min

First Order Homogeneous Differential Equations3 lectures • 16min

Bernoulli Differential Equations4 lectures • 30min

Differential Equations of the form dy/dx = f(Ax + By + C)4 lectures • 17min

Introduction to the Theory of Higher Order Equations5 lectures • 17min

Solving Higher Order Homogeneous Linear Differential Equations14 lectures • 46min

Finding the Differential Equation given the Solution6 lectures • 8min

Requirements

Description

Who this course is for: