Intro to Differential Equations (Edexcel A-Level Further Mathematics): Flashcards

Equation relating a function and its derivatives

D.E. with derivatives w.r.t. a single variable

D.E. with partial derivatives w.r.t. multiple variables

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

Separate variables and integrate

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

Use an integrating factor $F(x)$

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

$M(x, y) \, dx + N(x, y) \, dy = 0$

$\frac{\partial M}{\partial y} = \frac{\partial N}{\partial x}$