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Term 10 · Year 3

Term 10 — Differential Equations

1st and 2nd order ODEs, physical models, basic numerical methods.

10 lessons  ·  10 published ·  ~32h of study

(Year 3 — Integral, ODEs, Inference, Linear Algebra)

Classes (didactic grouping)

Each Class groups 2–5 Lessons by topic. Click on a Lesson to study the content.

Class A — Introduction and 1st-order separable/linear ODEs

~9h · 3 lessons
  1. Lesson 91
    Introduction to Ordinary Differential Equations
    y' = f(x,y), order, separability
    published →
  2. Lesson 92
    Separable ODEs
    y' = g(x)h(y), solution by integration
    published →
  3. Lesson 93
    1st-order linear ODEs
    y' + p(x)y = q(x), integrating factor
    published →

Class B — Growth, decay, Newton

~6h · 2 lessons
  1. Lesson 94
    Population models: Malthus and Verhulst
    Exponential growth, logistic, predator-prey
    published →
  2. Lesson 99
    Newton's Law of Cooling
    dT/dt = -k(T-Tₐ), real-world application
    published →

Class C — 2nd-order ODEs: vibrations and RLC

~9h · 3 lessons
  1. Lesson 95
    2nd-order linear ODEs with constant coefficients
    ay'' + by' + cy = 0, characteristic equation
    published →
  2. Lesson 96
    Mechanical vibrations: mass-spring-damper
    Spring-mass, free, damped, forced oscillations
    published →
  3. Lesson 97
    RLC Circuits
    Resistor + inductor + capacitor circuits, analogy with springs
    published →

Class D — Euler's method + synthesis

~6h · 2 lessons
  1. Lesson 98
    Euler's Method (Numerical)
    yₙ₊₁ = yₙ + h·f(xₙ,yₙ), error analysis
    published →
  2. Lesson 100
    Consolidation Quarter 10 (ODEs)
    Synthesis: 50 mixed ODE problems
    published →

Test yourself this term

There are 10 exam versions covering this term, each with answer key + step-by-step solutions. Take one after each group of lessons.

Open exams for Term 10 →