Rates of Change and Differential Equations
Unit 4, Topic 2 — Specialist Mathematics
Differential equations model real-world situations where a rate of change depends on the current state of a system. In this topic you will learn to set up, classify, and solve first-order differential equations, and apply them to population growth, cooling, mixing, and mechanical problems.
1
Related Rates of Change
Chain rule applications where multiple quantities change with time. Connecting rates using dy/dt = (dy/dx)(dx/dt).
2
Separable Differential Equations
Equations of the form dy/dx = f(x)g(y). Separate variables and integrate both sides to find general and particular solutions.
3
First-Order Linear Differential Equations
Equations of the form dy/dx + P(x)y = Q(x). Solved using the integrating factor μ = e^(∫P dx).
4
Applications of Differential Equations
Real-world models: logistic growth, Newton’s law of cooling, mixing problems, radioactive decay, and electrical circuits.