If $x^2+y^2=1$, then:

$y y''-\left(2 y'\right)^2+1=0$ $y''+\left(y'\right)^2+1=0$ $y y''-\left(y'\right)^2-1=0$ $y''+2\left(y'\right)^2+1=0$

$y''+\left(y'\right)^2+1=0$

$y^2=1-x^2 \Rightarrow 2 y y'=-2 x$ $\Rightarrow y y'=-x \Rightarrow y y''+y'+y'=-1$ $\Rightarrow y y''+\left(y'\right)^2+1=0$ Hence (2) is correct answer.