Chapter 7: Transcendental Functions - Section 7.4 - Exponential Change and Separable Differential Equations - Exercises 7.4 - Page 400: 17

$y=\sin (x^2+c)$

Rewrite the given equation and then integrate. We have $\int 2xdx= \int \dfrac{dy}{\sqrt {1-y^2}}$ This implies that $ \sin^{-1} (y)=x^2+c$ Also, $\sin (\sin^{-1} y)=\sin (x^2+c)$ Hence, $y=\sin (x^2+c)$