Numerical Methods in Context (AQA A-Level Mathematics): Flashcards

$a\frac{d^2y}{dx^2} + b\frac{dy}{dx} + cy = F(x)$

Solution to homogeneous equation ($F(x) = 0$)

Specific solution to non-homogeneous equation

Solve characteristic eqn assuming $y = e^{mx}$

C.F. + P.I.

$ax^2 + bx + c$

$ae^{kx}$

$a\sin\lambda x + b\cos\lambda x$

Multiply by $x$

$\lambda x e^{2x}$