Find multiple ODE solutions (counter example) I want to find some counter examples for the uniqueness of this ode
$$ \frac{dy}{dt} = t \sqrt{1-y^2}$$

and initial condition: $y(0)=1$
I don't have idea of how I should start to think, may someone give me a (some) clue(s)?
$y=1$ and $y=\sin\left(\frac{1}{2}t^2+\frac{\pi}{2}\right)$ both satisfy the initial condition $y(0)=1$
This is a separable DE:

$$ \frac{dy}{dt} = t \sqrt{1-y^2}$$

$=\frac{1}{\sqrt{1-y^2}} dy=t dt$

$sin^{-1}(y)+d=\frac{t^2}{2}+c$     (by integration)

$y= sin (\frac{t^2}{2} +a)$

Satisfy the equation for any $a$