I have this question: I'm not sure why the fourth option isn't showing up but hopefully it's not needed. When I separated the variables I got 2x^2=arcsint+C and when I solved for C I got the C=8. Is this right? It gave me option two, but I'm just not sure. :/ Thanks!
The identity you're looking for is $\displaystyle \sin^{-1}t=\frac{\pi}{2}-cos^{-1}t$, not $\displaystyle \sin^{-1}t=cos^{-1}t-\frac{\pi}{2}$. So #3 doesn't work.