Answer
$y=\arcsin x$
Work Step by Step
We need to integrate:
$y=\int \dfrac{dx}{\sqrt{1-x^2}}$
which can be integrated by using the differential trigonometric formula:
$\int \dfrac{dx}{\sqrt{x^2-a^2}}=\arcsin (x/a)+C$
$y=\arcsin x+c$
Take initial condition: $y(0)=0$
Then $y(0)=\arcsin (0)+c \implies c=0$
Thus, we have $y=\arcsin x$