What can be modelled with differential equations?
- Derivative terms like dy/dx are “rates of change”
- There are many situations that involve “change”
- Temperature
- Radioactivity
- Medication
- Sales
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:
- Important phrases here are …
- … “rate of change” – reference to a derivative term like dy/dx
- … directly/inversely proportional to – y = kx, y = 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
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
