| Exam Board | CAIE |
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| Module | FP1 (Further Pure Mathematics 1) |
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| Year | 2011 |
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| Session | June |
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| Topic | Second order differential equations |
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8 Find the general solution of the differential equation
$$\frac { \mathrm { d } ^ { 2 } x } { \mathrm {~d} t ^ { 2 } } + 2 \frac { \mathrm {~d} x } { \mathrm {~d} t } + 5 x = 10 \sin t$$
Find the particular solution, given that \(x = 5\) and \(\frac { \mathrm { d } x } { \mathrm {~d} t } = 2\) when \(t = 0\).
State an approximate solution for large positive values of \(t\).