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**twoteenine** $\displaystyle \frac{dy}{dx} \sqrt{1-x^{2}} = y^{2} , y(0) = 1$

I changed the equation to get

$\displaystyle \frac{dy}{y^2} = \frac{dx}{\sqrt{1-x^2}}$

Took the integral to get:

$\displaystyle -y^{-1} = sin^{-1}(x) + C$

I'm not sure what the rules with $\displaystyle sin^{-1}(x)$ are, but i got y by itself, ending with

$\displaystyle y = -\frac{1}{sin^{-1}(x)} + C$

When 0 is plugged in for x though, $\displaystyle \frac{1}{sin^{-1}(0)}$ goes to infinity. What did i do wrong?