9709 P33 - Nov 2014 - Q8
2338
The variables \(x\) and \(y\) are related by the differential equation \[ \frac{dy}{dx} = \frac{1}{5}x y^{\frac{1}{2}} \sin\left(\frac{1}{3}x\right). \]
(i) Find the general solution, giving \(y\) in terms of \(x\).
(ii) Given that \(y = 100\) when \(x = 0\), find the value of \(y\) when \(x = 25\).
