Differential Equations (Edexcel A-Level Mathematics): Flashcards

They represent a curve via $x$ and $y$ as functions of $t$.

$x = f(t)$ and $y = g(t)$, where $t$ is the parameter.

It defines both $x$ and $y$ as it varies.

Find a direct relationship $y = h(x)$ by substituting.

$dy/dx = (dy/dt) / (dx/dt)$ using the chain rule.

Area = $\int y \frac{dx}{dt} dt$.

They model motion or complex curves easily.

$x = 5t + 3$ and $y = 2t - 4$, defined for $0 ≤ t ≤ 5$.

Eliminate the parameter by substitution between equations.

Eliminate the parameter to express $y$ in terms of $x$.