AQA FP3 2013 January — Question 3

Exam BoardAQA
ModuleFP3 (Further Pure Mathematics 3)
Year2013
SessionJanuary
TopicSecond 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 $$\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } } - 2 \frac { \mathrm {~d} y } { \mathrm {~d} x } + y = 6 \mathrm { e } ^ { x }$$