Solve a first-order nonlinear ordinary differential equation with W|A?

[user2 (123 345)]

(dy/dx)^2 - Wolfram|Alpha)%2B1%3Dy%5E2

says (dy/dx)^2)+1=y^2 => y=cosh(x+c), y=cosh(x-c)

while it should be y=±cosh(x+c), y=±1

The two answers provided are same, and some results don’t show