Modelling with Differential Equations (Edexcel IAL Maths)

Spec point — 5.2

Modelling with differential equations

What can be modelled with differential equations?

• Derivative terms like $\frac{dy}{dx}$ 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 $\frac{dy}{dx}$

  • … directly/inversely proportional to ... $y=kx$, $y=\frac{k}{x}$

  • … 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

Exam Hint

• 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