| Exam Board | OCR |
|---|---|
| Module | FP3 (Further Pure Mathematics 3) |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Second order differential equations |
| Type | Standard non-homogeneous with exponential RHS |
| Difficulty | Standard +0.8 This is a standard second-order linear ODE with constant coefficients requiring the auxiliary equation method for the complementary function and particular integral by trial solution. While routine for FP3 students, it involves multiple steps (finding CF roots, determining PI form, solving for constants) and is from Further Maths, placing it moderately above average difficulty on an absolute scale. |
| 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
$$\frac{d^2y}{dx^2} - c\frac{dy}{dx} + 8y = e^{3x}.$$ [6]
\hfill \mbox{\textit{OCR FP3 Q3 [6]}}