First Order, Second Degree ODE

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SUMMARY

The discussion revolves around solving the first-order, second-degree ordinary differential equation (ODE) given by the equation y²(1 - (dy/dx)²) = 1. The user initially approached the problem by expressing dy/dx and considering two cases, yielding y² = 1 + (x+C)² and y² = 1 + (-x+C)². A professor suggested that this ODE is well-known and hinted at a trigonometric substitution, specifically y = sin(z), as a potential method for solving it.

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

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