Differential Equations (AQA A-Level Further Maths): Flashcards

Equation with only first derivative like $\frac{dy}{dx}$

Rearrange: all $x$ terms one side, all $y$ terms other side

When equation cannot be separated into distinct $x$ & $y$ terms

Left side recognised as derivative of a product

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

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

Solution with constant $c$, represents family of curves

Solution with specific $c$ from initial conditions

Must equal 1

Transform complex equation into simpler, solvable form