(a) Show that an appropriate integrating factor for
\[\left(x^{2}+1\right) \frac{\mathrm{d} y}{\mathrm{~d} x}+y \sqrt{x^{2}+1}=x^{2}-x \sqrt{x^{2}+1}\]
is \(x+\sqrt{x^{2}+1}\).
(b) Hence find the solution of the differential equation
\[\left(x^{2}+1\right) \frac{\mathrm{d} y}{\mathrm{~d} x}+y \sqrt{x^{2}+1}=x^{2}-x \sqrt{x^{2}+1}\]
for which \(y=\ln 2\) when \(x=0\). Give your answer in the form \(y=\mathrm{f}(x)\).