## Ordinary Differential Equations

- Definition of a Differential Equation with Classification of Type and Notation
- Classification of Order with Six Examples
- Classification of Linearity with Four Examples
- Ten Examples of stating Order and Determining Linear or Nonlinear
- Overview of Differential Form and Definitions regarding Solutions to Differential Equations
- Example #1 – Verify the given function is the general solution of the ODE
- Example #2 – Verify the given function is the general solution of the ODE
- Example #3 – Verify the given function is the general solution of the ODE
- Example #4 – Verify the given function is the general solution of the ODE

## Initial Value Problems

- Quick Review of Solutions of a Differential Equation and Steps for an IVP
- Example #1 – find the value(s) of m that Satisfy the Differential Equation
- Example #2 – verify the given function is the general solution of the ODE
- Example #3 – for a One-Parameter Family, find the solution to the IVP
- Example #4 – for a Two-Parameter Family, find the solution to the IVP
- Example #5 – for a Two-Parameter Family, find the solution to the IVP
- Existence of Uniqueness Theorem and Interval of Existence
- Two Examples – Determine whether the Uniqueness/Existence Theorem implies the IVP has a unique solution
- Example – Give the Largest Interval over which the Solution is Defined
- Example – Give the Largest Interval over which the Solution is Defined
- Example – Give the Largest Interval over which the Solution is Defined