Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2022 / Paper 2 / 15 / a / ii / Solution

Again $C=0$. Since the initial sine is nonzero, the local branch must satisfy $\sin y=x$. Selecting the inverse-sine branch through $y=\pi /6$ givesThis passes through the specified point and has $y^{\prime }=1/\sqrt{1-x^2}$, which verifies the original equation on this interval.