Answer
$y= Ce^{\frac{2}{3}x^{\frac{3}{2}}} $
Work Step by Step
Separate the variables into x's and y's on each side.
$\frac{dy}{dx}= \sqrt x y$
$\frac{1}{y}dy= \sqrt x dx$
$ \int \frac{1}{y}dy=\int \sqrt x dx$
$ \ln|y| = \frac{2}{3}x^{\frac{3}{2}} +C$,
Exponentiate and Let $e^C=C$
$y=Ce^{\frac{2}{3}x^{\frac{3}{2}}}$
