I used the method that says that istead of " y' " I can place " p " and istead of " y'' "
I can place " p*(dp/dy) ".
Then i got a easy saprable eqation but it doesnt see correct according to my booklet.
One thing I see. You let
$\displaystyle \text{arcsinh}(y) = \dfrac{e^y - e^{-y}}{2}$
but
$\displaystyle \text{sinh}(y) = \dfrac{e^y - e^{-y}}{2}$.
I'm surprised that your book didn't give the explicit solution
$\displaystyle y = \sqrt{2} \sinh x + \cosh x$.