Further MathsYears 12–13Differential Equations

First-order differential equations

Solve separable and first-order linear ODEs using integrating factors; model real-world problems

What you'll learn

  1. 1

    Imagine you're driving a 🚗 and your speed changes every second — the speedometer shows your speed, but what if you want to know how fast your speed is changing? That's a differential equation!

  2. 2

    What does a differential equation tell us about?

  3. 3

    Let's solve a simple one: dy/dx = 2x. Drag the antiderivative pieces together to build the solution!

  4. 4

    Solve dy/dx = 3x² step by step.

  5. 5

    What is the general solution to dy/dx = 4x³?

  6. 6

    Now you try: solve dy/dx = 6x. Use the slider to find the antiderivative!

  7. 7

    The solution to dy/dx = 6x is y = ?

Practise First-order differential equations with Whizlo

Free AI-tutored lessons, unlimited practice questions, and progress tracking for ages 16–18. Aligned to the UK National Curriculum.