Seperable Differential Equation

We covered this last Tuesday, and had an exam on Thursday, so instead of doing HW I studied for the exam. I am a little confused on DE, and forgot a bit of what we went over in class. Could you check my work, please?

$\displaystyle

\frac{dy}{dx}=\frac{\sqrt{x}}{e^y}$

$\displaystyle e^y dy= \sqrt{x}dx$

$\displaystyle \int e^y dy= \int \sqrt{x}dx$

$\displaystyle e^y= \frac{2}{3}x^\frac{3}{2} + C$

$\displaystyle ylne=\frac{2}{3}x^\frac{3}{2} + C$

$\displaystyle y=ln(\frac{2}{3}x^\frac{3}{2} + C)$

Thank you.