CIE A Level Maths: Pure 3

Revision Notes

A LevelMaths: Pure 3CIERevision Notes5. Integration5.2 Differential Equations5.2.4 Modelling with Differential Equations

5.2.4 Modelling with Differential Equations

Test Yourself

Modelling with Differential Equations

What can be modelled with differential equations?

Derivative terms like $\frac{d y}{d x}$ are “rates of change”
There are many situations that involve “change”

- Temperature
- Radioactivity
- Medication
- Sales

Notes de_scenes, AS & A Level Maths revision notes

How do I set up a model with differential equations?

The first task is to set up a differential equation from a description in words:

Notes de_setup, AS & A Level Maths revision notes

Important phrases here are …
- … “rate of change” ... reference to a derivative term like $\frac{d y}{d x}$
- … directly/inversely proportional to ... $y = k x$ , $y = \frac{k}{x}$
- … formulate ... means to write as an equation
  - you may need to choose and define letters for variables
  - V for volume, h for height (of a cylinder, say)

Some differential equations may involve Connected Rates of Change

Notes de_croc_setup, AS & A Level Maths revision notes

Exam Tip

Use a highlighter (or underline) to pick out important words/phrases
Read and re-read the question several times
Jot down bits and pieces as you go; do not expect to go straight from reading to writing down a differential equation.

Worked example

Example soltn, AS & A Level Maths revision notes

You've read 0 of your 0 free revision notes

Get unlimited access

to absolutely everything:

Downloadable PDFs
Unlimited Revision Notes
Topic Questions
Past Papers
Model Answers
Videos (Maths and Science)

Join the 100,000+ Students that ❤️ Save My Exams

the (exam) results speak for themselves:

Test yourself Next topic

Did this page help you?

Author: Paul

Paul has taught mathematics for 20 years and has been an examiner for Edexcel for over a decade. GCSE, A level, pure, mechanics, statistics, discrete – if it’s in a Maths exam, Paul will know about it. Paul is a passionate fan of clear and colourful notes with fascinating diagrams – one of the many reasons he is excited to be a member of the SME team.