Second Order Equations (AQA A-Level Further Maths): Flashcards

Has $\frac{d^2y}{dx^2}$ but no higher derivatives

Right-hand side equals zero: $f(x) = 0$

Quadratic $am^2 + bm + c = 0$ from assuming $y = Ce^{mx}$

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

$y = (Ax + B)e^{mx}$

$y = e^{mx}(A\cos nx + B\sin nx)$

Solution to the homogeneous equation

Specific function for the full non-homogeneous equation

GS = CF + PI

Multiply the trial function by $x$