First order differential equations (integrating factor)
7
Show that \(\frac { \mathrm { d } } { \mathrm { d } x } ( \ln ( \tanh x ) ) = 2 \operatorname { cosech } 2 x\).
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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.