Use separation of variables to solve the IVP

How would you go about doing this? So far I've done this:

$\displaystyle dy/\sqrt(1-y^2) = dt/t$

$\displaystyle arcsin(y) = ln(t) +c$

I don't know if my work is correct, but would the solution just be $\displaystyle y=sin(ln(t))?$