Learning Objectives:

__Math Tutoring on Second Order Differential Equations__

A ** Second Order Ordinary Differential Equation** has the form:

If the **Second Order Differential Equation** can be written in the form:

Then the **Differential Equation** is a **Linear Second Order Differential Equation.** If it does not fit in the above form it is **Nonlinear**.

If **,** the **Linear Second Order DE is Homogeneous****. **If **,** it is **Nonhomogeneous.**

*Solutions to Linear Second Order Homogeneous DEs using the Characteristic Equation*

1. If are two **distinct real roots** then

2. If are **real and equal roots** then

3. If are two **complex roots ** then

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**Hook Questions:**

*1. **Define **Second Order Differential Equations**.*

*2. **What is **Characteristics Equations?*

*3. **What are the different **Solutions to Linear Second Order Homogeneous DEs using the Characteristic Equation?*

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