# Math Help - Secound Order differential equation

1. ## Secound Order differential equation

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.

2. One thing I see. You let

$\text{arcsinh}(y) = \dfrac{e^y - e^{-y}}{2}$

but

$\text{sinh}(y) = \dfrac{e^y - e^{-y}}{2}$.

I'm surprised that your book didn't give the explicit solution
$y = \sqrt{2} \sinh x + \cosh x$.

thanks!