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.
15
- 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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[7 marks]
15 - Find the maximum height of the column of water, giving your answer to the nearest cm .
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[1 mark]