Learning Objectives:

__Math Tutoring on Introduction to Differential Equations__

A **Differential Equation** is an equation that contains an unknown function and its derivative.

**e.g. ** etc.

To solve a** Differential Equation****,** we want to determine an equation that satisfies the **Derivative Equation****.** This will require Integration.

When solving a **Differential Equation** in the form **,** it is helpful to rewrite the equation in **Differential Form****.** Then we can integrate both sides of the equation.

__Types of Differential Equations:__

1. ** Ordinary Differential Equations (ODE**) – An

2. ** Partial Differential Equations (PDE)** – A

** The Order of a Differential Equation (ODE or PDE)** – The

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*Linear and Nonlinear Differential Equations:*

1. A **Linear Differential Equation** can be written in the form:

Note that –

· The **Dependent Variable** and all of its derivatives are always to the first power.

· There are no products of the function **‘ y’** and its derivatives.

· The coefficients can be zero, constants, or functions of **‘ t’**.

2. A **Nonlinear Differential Equation** is a **Differential Equation** that is ** NOT** linear.

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**Hook Questions:**

*1. **What is **Differential Equations**? How to solve it?*

*2. **What are the **Ordinary and Partial Differential Equations**?*

*3. **What is **Linear Differential Equation**? State some properties of it. *

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