(A Level) Differential equations

Learning objectives

Form a first-order differential equation from a statement about a rate of change, introducing a constant of proportionality k where needed

Solve a differential equation with separable variables, dy/dx = f(x)g(y), by rearranging to ∫ 1/g(y) dy = ∫ f(x) dx, using partial fractions, integration by parts or a substitution where necessary

Fix the arbitrary constant from an initial condition to obtain the particular solution, and rearrange it to give y explicitly in terms of x when asked

Interpret a solution in its context, for example the long-term behaviour of a population, the time for a quantity to halve or the limiting value as t → ∞