Hyperbolic function manipulation then solve

A question is this type if and only if it requires first simplifying or proving a hyperbolic identity before solving the differential equation.

1 questions · Challenging +1.2

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Show that $( \cosh x + \sinh x ) ^ { \frac { 1 } { 2 } } = \mathrm { e } ^ { \frac { 1 } { 2 } x }$.
Find the particular solution of the differential equation $$\frac { d ^ { 2 } y } { d x ^ { 2 } } + \frac { d y } { d x } + 3 y = 5 ( \cosh x + \sinh x ) ^ { \frac { 1 } { 2 } }$$ given that, when $x = 0 , y = 1$ and $\frac { d y } { d x } = \frac { 4 } { 3 }$.