General Solutions (AQA A-Level Mathematics): Flashcards

Most general form of solution with arbitrary constants

First derivative $\frac{dy}{dx}$

Up to second derivative $\frac{d^2y}{dx^2}$

Infinite set of solutions

Variables can be separated on either side

Separate variables, integrate both sides

$C$

Characteristic equation

$y = C_1 e^{m_1 x} + C_2 e^{m_2 x}$

$\frac{dy}{dx} = f(x, y)$