| Exam Board | Edexcel |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Marks | 9 |
| Paper | 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 (solving auxiliary equation with irrational roots) and particular integral (using undetermined coefficients method with trigonometric forcing). While the method is standard for FP2, the non-repeated irrational roots and trigonometric particular integral make this moderately challenging, requiring careful algebraic manipulation across multiple steps for 9 marks. |
| Spec | 4.10e Second order non-homogeneous: complementary + particular integral |
Find the general solution of the differential equation
$$\frac{d^2 x}{dt^2} + 6 \frac{dx}{dt} + 6x = 2 \cos t - \sin t.$$ [9]
\hfill \mbox{\textit{Edexcel FP2 Q4 [9]}}