1 A curve passes through the point \(( 9,6 )\) and satisfies the differential equation $$\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { 1 } { 2 + \sqrt { x } }$$ Use a step-by-step method with a step length of 0.25 to estimate the value of \(y\) at \(x = 9.5\). Give your answer to four decimal places.
[0pt] [5 marks]