| Exam Board | AQA |
| Module | FP3 (Further Pure Mathematics 3) |
| Year | 2013 |
| Session | January |
| Topic | Second order differential equations |
3 It is given that the general solution of the differential equation
$$\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } } - 2 \frac { \mathrm {~d} y } { \mathrm {~d} x } + y = 0$$
is \(y = \mathrm { e } ^ { x } ( A x + B )\). Hence find the general solution of the differential equation
$$\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } } - 2 \frac { \mathrm {~d} y } { \mathrm {~d} x } + y = 6 \mathrm { e } ^ { x }$$