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

$a\frac{d^2y}{dx^2} + b\frac{dy}{dx} + cy = 0$

$am^2 + bm + c = 0$

$b^2 - 4ac > 0$

$y = Ae^{m_1x} + Be^{m_2x}$

$b^2 - 4ac = 0$

$y = (A + Bx)e^{mx}$

$b^2 - 4ac < 0$

$y = e^{\alpha x}(A\cos(\beta x) + B\sin(\beta x))$

$y = y_c + y_p$

Complementary function (solution to homogeneous equation)