You're differentiating sin^-1y with respect to x, so you use the chain rule and first differentiate with respect to y, then derive y with respect to x, then multiply the two derivatives together. That would give you 1/sqrt(1-y^2) * dy/dx, not 1/sqrt(1-x^2) *dy/dxx^2+xsin^-1y=ye^x
2x+xy'/(1-x^2)^(1/2)+sin^(-1)y=ye^x+y'e^x