Standard +0.3 This is a separable differential equation requiring standard integration techniques (separation of variables, integrating √x and sin 2t, applying initial conditions). While it involves 7 marks suggesting multiple steps, the method is routine for Further Maths students with no conceptual challenges or novel problem-solving required—slightly easier than average.
The height \(x\) metres, of a column of water in a fountain display satisfies the differential equation \(\frac{dx}{dt} = -\frac{8\sin 2t}{3\sqrt{x}}\), 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 \(x = f(t)\)
[7 marks]
The height $x$ metres, of a column of water in a fountain display satisfies the differential equation $\frac{dx}{dt} = -\frac{8\sin 2t}{3\sqrt{x}}$, 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 $x = f(t)$
[7 marks]
\hfill \mbox{\textit{SPS SPS FM Pure 2021 Q15 [7]}}