Separation of Variables (AQA A-Level Mathematics): Flashcards

Solves 1st-order diff. eqs. by separating x and y terms

When eq. can be rewritten with all y one side, all x other side

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

Arrange all $y$ terms (with $dy$) one side, $x$ terms other

Integrate both sides w.r.t. their respective variables

Constant of integration ($C$)

$\frac{1}{h(y)} dy = g(x) dx$

Exponentiate both sides

Solution not solved explicitly for $y$

Growth & decay, motion, fluid flow