Hi,

I have the following equation $\displaystyle \frac{dy}{dt}=t\sqrt{1-y^2} $

I found solutions $\displaystyle *S:=\{1 , cos(t^2)\} $.

I don't really get why it would not violate the existence and uniqueness theorem.

I would have $\displaystyle R = \{(t,y), -\infty < t < \infty, -1 < y < 1 \} $.

Isn't f and f' continuous on R? If yes it should thus admit one solution.