| Exam Board | CAIE |
|---|---|
| Module | FP1 (Further Pure Mathematics 1) |
| Year | 2005 |
| Session | November |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Second order differential equations |
| Type | Particular solution with initial conditions |
| Difficulty | Standard +0.3 This is a standard second-order linear differential equation with constant coefficients and an exponential forcing term. The method is routine: find the complementary function (solving a quadratic auxiliary equation), find a particular integral (trying y = Ae^{2x}), apply initial conditions to find constants. While it requires multiple steps and is from Further Maths, the technique is entirely procedural with no novel insight required, making it slightly easier than average overall. |
| Spec | 4.10d Second order homogeneous: auxiliary equation method4.10e Second order non-homogeneous: complementary + particular integral |
Solve the differential equation
$$\frac{d^2y}{dx^2} + 3\frac{dy}{dx} + 2y = 24e^{2x},$$
given that $y = 1$ and $\frac{dy}{dx} = 9$ when $x = 0$. [7]
\hfill \mbox{\textit{CAIE FP1 2005 Q4 [7]}}