| Exam Board | CAIE |
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| Module | FP1 (Further Pure Mathematics 1) |
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| Year | 2017 |
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| Session | June |
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| Topic | Second order differential equations |
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8 Find the solution of the differential equation
$$\frac { \mathrm { d } ^ { 2 } x } { \mathrm {~d} t ^ { 2 } } + 6 \frac { \mathrm {~d} x } { \mathrm {~d} t } + 9 x = 18 t ^ { 2 } + 6 t + 1$$
given that, when \(t = 0 , x = 3\) and \(\frac { \mathrm { d } x } { \mathrm {~d} t } = 0\).