Answer
$$2\tan \sqrt y = x + C$$
Work Step by Step
$$\eqalign{
& \frac{{dy}}{{dx}} = \sqrt y {\cos ^2}\sqrt y \cr
& {\text{Separating the variables gives}} \cr
& \frac{{dy}}{{\sqrt y {{\cos }^2}\sqrt y }} = dx \cr
& {\text{use the identity sec}}\theta = \frac{1}{{\cos \theta }} \cr
& \frac{{{{\sec }^2}\sqrt y }}{{\sqrt y }}dy = dx \cr
& {\text{integrating}} \cr
& \int {\frac{{{{\sec }^2}\sqrt y }}{{\sqrt y }}} dy = \int {dx} \cr
& 2\int {{{\sec }^2}\sqrt y \left( {\frac{1}{{2\sqrt y }}} \right)} dy = \int {dx} \cr
& 2\tan \sqrt y = x + C \cr} $$
