Solving First Order Differential Equations (Edexcel A-Level Further Mathematics): Flashcards

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

Rewrites equation in new variables to simplify and make solvable

Back-substitute original variables

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

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

$r' \sin \theta + r \cos \theta = 0$

$r' \cos \theta - r \sin \theta = 0$

$\frac{r'\sin\theta + r\cos\theta}{r'\cos\theta - r\sin\theta}$

$\frac{d}{dx}[F(x)y] = F(x)Q(x)$

$A = \frac{1}{2} \int_\alpha^\beta r^2 \, d\theta$