| Exam Board | OCR |
|---|---|
| Module | FP3 (Further Pure Mathematics 3) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Second order differential equations |
| Type | Standard non-homogeneous with trigonometric RHS |
| Difficulty | Standard +0.8 This is a second-order linear ODE with constant coefficients requiring both complementary function (complex roots: -2±i) and particular integral using undetermined coefficients method with sin/cos terms. While the technique is standard for FP3, it involves multiple steps: finding auxiliary equation roots, writing CF with complex exponentials or equivalent form, finding PI coefficients by substituting and equating, then combining. The arithmetic with the particular integral is moderately involved but follows a well-practiced algorithm, making it harder than average A-level but routine for Further Maths students. |
| 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
$$\frac{d^2y}{dx^2} + 4\frac{dy}{dx} + 5y = 65 \sin 2x.$$ [9]
\hfill \mbox{\textit{OCR FP3 Q4 [9]}}