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LearnCambridge97092026–2027Paper 3 · Pure Mathematics 3Differential equations
Paper 3 · Module

Differential equations

4 subtopics≈ 155 min in total
Start the module: Forming differential equationsOpen graphing calculator

  1. Forming differential equations

    Turn words about change into mathematics. "Grows in proportion to", "decreases at a rate inversely proportional to", "flows in and leaks out": each becomes an equation for a derivative, ready to solve.

    ≈ 30 min

  2. Separating the variables

    Gather every yy with dydy on one side and every xx with dxdx on the other, integrate, and add one constant. The method that solves almost every Paper 3 differential equation.

    ≈ 35 min

  3. Particular solutions with harder integrals

    Exam differential equations are integration questions in disguise. Once the variables are separated, one side often needs partial fractions, integration by parts or a trigonometric identity. Bring all of Paper 3 integration to bear, then pin down the constant.

    ≈ 45 min

  4. Modelling with differential equations

    Populations, cooling drinks, draining tanks and spreading rumours. Solve the equation, use two pieces of data to fix the constants, and then ask the real questions: when, how much, and what happens in the long run?

    ≈ 45 min