Solving & Interpreting Differential Equations (AQA A-Level Mathematics): Flashcards

The first derivative of the unknown function

$\frac{dy}{dx} = g(x)h(y)$

$\frac{dy}{dx} + P(x)y = Q(x)$

$IF = e^{\int P(x) \, dx}$

The second derivative of the unknown function

$\frac{d^2y}{dx^2} + p\frac{dy}{dx} + qy = 0$

Find particular solution & specific values of constants

Nature of roots (real distinct, repeated, or complex)

Stability of system & long-term predictions of model

Initial population and growth rate