| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9795 (Pre-U Further Mathematics) |
| Session | Specimen |
| Topic | Second order differential equations |
| Type | Standard non-homogeneous with exponential RHS |
| Difficulty | Standard +0.3 This is a standard second-order linear differential equation with constant coefficients and exponential RHS. The auxiliary equation gives a repeated root (-3), requiring complementary function y_c = (A + Bx)e^(-3x). The particular integral uses trial solution Ce^(3x), which doesn't overlap with the CF, making substitution straightforward. While it requires multiple techniques (auxiliary equation, particular integral, combining solutions), these are routine procedures for this topic with no conceptual surprises. |
| Spec | 4.10e Second order non-homogeneous: complementary + particular integral |
5 Find the general solution of the differential equation
$$\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } } + 6 \frac { \mathrm {~d} y } { \mathrm {~d} x } + 9 y = 72 \mathrm { e } ^ { 3 x }$$
\hfill \mbox{\textit{Pre-U Pre-U 9795 Q5}}