| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9795 (Pre-U Further Mathematics) |
| Session | Specimen |
| Marks | 7 |
| Topic | Second order differential equations |
| Type | Standard non-homogeneous with exponential RHS |
| Difficulty | Standard +0.8 This is a second-order linear ODE with constant coefficients requiring the auxiliary equation method for the complementary function (which yields a repeated root case) and particular integral by trial solution. While systematic, it involves multiple technical steps including handling the repeated root λ=-3 and finding a PI for the exponential forcing term, making it moderately challenging but still a standard Further Maths technique. |
| 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
$$\frac{\mathrm{d}^2 y}{\mathrm{d}x^2} + 6\frac{\mathrm{d}y}{\mathrm{d}x} + 9y = 72\mathrm{e}^{3x}.$$ [7]
\hfill \mbox{\textit{Pre-U Pre-U 9795 Q5 [7]}}