| Exam Board | OCR |
|---|---|
| Module | FP3 (Further Pure Mathematics 3) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Second order differential equations |
| Type | Standard non-homogeneous with polynomial RHS |
| Difficulty | Standard +0.3 This is a standard second-order linear ODE with constant coefficients and a polynomial forcing term. The auxiliary equation gives a repeated root (m=4), requiring the complementary function y_c = (A+Bx)e^(4x), and the particular integral is found by trying y_p = ax+b. While it's Further Maths content, the method is entirely routine and algorithmic with no conceptual challenges, making it slightly easier than an average A-level question overall. |
| Spec | 4.10d Second order homogeneous: auxiliary equation method4.10e Second order non-homogeneous: complementary + particular integral |
Find the general solution of the differential equation
$$\frac{d^2y}{dx^2} - 8\frac{dy}{dx} + 16y = 4x.$$ [7]
\hfill \mbox{\textit{OCR FP3 Q2 [7]}}