Calculus of a Single Variable, Chapter 6, 6.4, Section 6.4, Problem 54

Given y' = 2xsqrt(1-y^2)
=> dy /dx = 2xsqrt(1-y^2)
=> (1/(sqrt(1-y^2)))dy = 2xdx
integrating on both sides we get
int (1/(sqrt(1-y^2)))dy = int 2xdx
as we know that int (1/sqrt(1-y^2))dy= sin^-1 y
sin^-1 (y)=x^2+c
y=sin(x^2+c)