# Differential Equations

**Differential equations** are a special type of **integration** problem.

Here is a simple differential equation of the type that we met earlier in the Integration chapter:

`(dy)/(dx)=x^2-3`

We didn't call it a differential equation before, but it is one. We'll see several different types of differential equations in this chapter.

## In this Differential Equations Chapter

### Why are we doing this?

There are many applications of differential equations, including:

In this chapter we will learn about:

### Definition and Solution of DEs

- Predicting AIDS - a DEs example
- 1. Solving Differential Equations, write equations in differential form, solve simple differential equations and recognise different types of differential equations
- 2. Separation of Variables - a method of solving differential equations
- 3. Integrable Combinations - a method of solving differential equations
- 4. Linear DEs of Order 1 - and how to solve them

### Applications - Electronics

- 5. Application: RL Circuits - containing a resistor and inductor
- 6. Application: RC Circuits - containing a resistor and capacitor

### Second Order Differential Equations

- 7. Second Order DEs - Homogeneous - definition and method of solution
- 8. Second Order DEs - Damping - RLC - in a circuit with resistor, inductor and capacitor
- 9. Second Order DEs - Forced Response - constant and non-constant driving forces
- 10. Second Order DEs - Solve Using SNB - solving DEs using a computer algebra system

Before we see how to solve differential equations, let's see an example of them in action in the AIDS example.

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