First Order, Second Degree ODE

[ong_jun_jie]

Homework Statement

Solve y^2*(1-(dy/dx)^2)=1

Homework Equations

The Attempt at a Solution

I expressed the ODE in terms of dy/dx and considered two cases. I got

(a) y^2 = 1 + (x+C)^2
(b) y^2 = 1 + (-x+C)^2 where C is a constant

However, my professor told me that there is another way to do this. He hinted me that this was some well-known ODE. Can someone enlighten me on where to find out more about this ODE? Thank you.

 

[clamtrox]

That looks suspiciously like something trigonometric. Perhaps you could do a change of variables y=sin(z) or something similar.