A Level Maths: Differential Equations Topic Summary and Resources
Video Lessons
Watch alongside the worksheet for the full lesson experience, then test your understanding with the lesson questions.
Revision Notes
Handwritten notes summarising the key ideas for each lesson. Ideal for quick review before a test.
Exam Questions
Past-paper-style questions organised by topic, with full mark schemes.
Drawn from OCR and Edexcel past papers but designed to be useful for students of all UK exam boards — including AQA and OCR MEI — unless a sheet is explicitly board-specific.
Before You Start This Topic
It will help if you are confident with the following:
- Integration — foundational
- Further Integration — often needed for the integrals that arise
- Exponentials and Logarithms — ln integration is central
A Level Maths differential equations combines all your calculus skills with modelling. A differential equation relates a function to its derivatives — for example, $\frac{dy}{dt} = -ky$ describes exponential decay. Solving such equations gives you the function, which you then interpret in the original problem's context. This topic ties together Integration, Further Integration, and Connected Rates of Change.
You solve first-order separable differential equations by separating the variables — moving all $y$-terms (and $dy$) to one side and all $x$-terms (and $dx$) to the other — then integrating both sides. You apply an initial condition to fix the constant of integration, giving a particular solution. You use differential equations to model exponential growth and decay, Newton's law of cooling, mixing problems, and population models. You also interpret solutions in context, identify limitations of the model (often as $t$ becomes large), and consider how to refine the model when its predictions become unrealistic.
Differential equations is part of the Pure Maths strand of A Level Maths for AQA, Edexcel, OCR, and OCR MEI students.
Watch out for…
A few things to be careful with: not every differential equation is separable — check that you can split into $f(y) \, dy = g(x) \, dx$ form; do NOT forget the constant of integration, and use the initial condition to find it; when integrating something like $\frac{dy}{y}$, the result is $\ln|y| + c$ — the absolute value matters; and check your solution by differentiating to confirm it satisfies the original equation — this catches many errors.