So I am getting stuck trying to solve this. pgA and Tx are constants
d^2h/dx^2 = (pgA/Tx)*sqrt(1+(dh/dx)^2)
I substitute dh/dx = sinh(u), d^2h/dx^2 = coshu(du/dx)
then you get (pgA/Tx)*cosh(u) = cosh(u)(du/dx)
... and I'm unsure where to go after this. I tried a couple more things but I'm not sure if it's the right track:
(pgA/Tx) * cosh(u) = cosh(u)(du/dx) ... integrate and solve for u = (pgAx/Tx)+C
and then substitute back in for u??? Sorry this isn't in Latex but I couldn't figure it out.