The following video provides an outline of all the topics you would expect to see in a typical Differential Equations class (i.e., **Ordinary Differential Equations**, ODE, DEs, Diff-Eq, or Calculus 4).

All of the topics are covered in detail in our Online Differential Equations Course. The course contains full lectures along with detailed examples.

## Differential Equations Overview

Differential Equations Overview

## Intro to DiffEqs

- Ordinary Differential Equations
- Initial Value Problems

## First Order Differential Equations

- Directional Fields
- Separable Equations
- Solving Exact ODEs
- Homogeneous Differential Equation
- Bernoulli Differential Equation
- Linear and Nonlinear Models

## Second Order Differential Equations

- Distinct Real Roots
- Complex Roots
- Repeated Roots
- Wronskian
- Undetermined Coefficients
- Differential Operators
- Variation of Parameters
- Cauchy Euler Equation
- Predator Prey Models and Electrical Networks
- Mechanical Vibrations

## Laplace Transform

- Laplace Transform Overview
- Inverse Laplace Transforms
- Initial Value Problems with Laplace Transforms
- Translation Theorems of Laplace Transforms

## Systems of Differential Equations

- Phase Plane Portraits
- Homogeneous Linear Systems

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