(a) Show that an appropriate integrating factor for
\(\sqrt{x^{2}-1} \frac{\mathrm{~d} y}{\mathrm{~d} x}+y=x^{2}-x \sqrt{x^{2}-1}\)
is \(x+\sqrt{x^{2}-1}\).

(b) Hence find the solution of the differential equation
\(\sqrt{x^{2}-1} \frac{\mathrm{~d} y}{\mathrm{~d} x}+y=x^{2}-x \sqrt{x^{2}-1}\)
for which \(y=1\) when \(x=\frac{5}{4}\). Give your answer in the form \(y=\mathrm{f}(x)\).