#### Answer

$y= \sin ^{-1}(\frac{x^{2}}{2}+C) $

#### Work Step by Step

$\frac{dy}{dx}=x\sec y$
Separating the variables, we have
$\frac{dy}{\sec y}=xdx$
or $\cos y \, dy=xdx$
Integrating both sides, we get
$\int\cos y\,dy=\int xdx$
$\sin y=\frac{x^{2}}{2}+C$
or $y=\sin^{-1}(\frac{x^{2}}{2}+C)$ where C is an arbitrary constant.