| Exam Board | SPS |
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| Module | SPS FM Pure (SPS FM Pure) |
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| Year | 2021 |
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| Session | June |
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| Marks | 7 |
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| Topic | Differential equations |
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15. The height \(x\) metres, of a column of water in a fountain display satisfies the differential equation \(\frac { \mathrm { d } x } { \mathrm {~d} t } = \frac { 8 \sin 2 t } { 3 \sqrt { x } }\), where \(t\) is the time in seconds after the display begins.
Solve the differential equation, given that initially the column of water has zero height.
Express your answer in the form \(x = \mathrm { f } ( t )\)
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