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

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.