| Exam Board | Edexcel |
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| Module | FP2 (Further Pure Mathematics 2) |
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| Year | 2004 |
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| Session | June |
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| Topic | Second order differential equations |
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8. (a) Find the general solution of the differential equation
$$\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} t ^ { 2 } } + 2 \frac { \mathrm {~d} y } { \mathrm {~d} t } + 2 y = 2 \mathrm { e } ^ { - t }$$
(b) Find the particular solution that satisfies \(y = 1\) and \(\frac { \mathrm { d } y } { \mathrm {~d} t } = 1\) at \(t = 0\).
(6)(Total 12 marks)