First order differential equations (integrating factor)
6
Starting from the definitions of sinh and cosh in terms of exponentials, prove that
$$2 \sinh ^ { 2 } x = \cosh 2 x - 1$$
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Find the solution to the differential equation
$$\frac { d y } { d x } + y \operatorname { coth } x = 4 \sinh x$$
for which \(y = 1\) when \(x = \ln 3\).