# 8.3.4 Modelling with Differential Equations

A Level Only

#### What can be modelled with differential equations?

• Derivative terms like dy/dx are “rates of change”

• There are many situations that involve “change”
• Temperature
• 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.

Jot down bits and pieces as you go; do not expect to go straight from reading to writing down a differential equation.

A Level Only

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