(a) Show that \(\frac{\mathrm{d}}{\mathrm{d} x}(\ln (\tanh x))=2 \operatorname{cosech} 2 x\).

(b) Find the solution of the differential equation
\(\sinh 2 x \frac{\mathrm{~d} y}{\mathrm{~d} x}+2 y=\sinh 2 x\)
for which \(y=5\) when \(x=\ln 2\). Give your answer in an exact form.