| Exam Board | CAIE |
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| Module | FP1 (Further Pure Mathematics 1) |
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| Year | 2014 |
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| Session | June |
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| Topic | Second order differential equations |
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10 Find the particular solution of the differential equation
$$\frac { \mathrm { d } ^ { 2 } x } { \mathrm {~d} t ^ { 2 } } + 0.16 \frac { \mathrm {~d} x } { \mathrm {~d} t } + 0.0064 x = 8.64 + 0.32 t$$
given that when \(t = 0 , x = 0\) and \(\frac { \mathrm { d } x } { \mathrm {~d} t } = 0\).
Show that, for large positive \(t , \frac { \mathrm {~d} x } { \mathrm {~d} t } \approx 50\).