(a) Show that
\(\frac{\mathrm{d}}{\mathrm{~d} x}\left(\frac{x}{2} \sqrt{x^{2}-9}-\frac{9}{2} \cosh ^{-1} \frac{x}{3}\right)=\sqrt{x^{2}-9} .\)
(b) Find the solution of the differential equation
\(x \frac{\mathrm{~d} y}{\mathrm{~d} x}-y=x^{2} \sqrt{x^{2}-9}\)
given that \(y=1\) when \(x=3\). Give your answer in the form \(y=\mathrm{f}(x)\).