Last question of the day on differential equations

So I have this problem which states use separation of variables to find the general solution of the differential equation.

$\displaystyle \frac{dy}{dx}=\sqrt\frac{x}{y}$ so to start, I'll move the dx to the other side to get:

$\displaystyle dy=\sqrt\frac{x}{y}dx$

Now, to get rid of the square root, can I simply square both sides to get:

$\displaystyle d^{2}y=\frac{x}{y}dx^2$ then divide by y to get:

$\displaystyle \frac{1}{y}d^{2}y=xdx^{2}$

And then from there, integrate both sides twice? The only issue I see is after integrating once, I get:

$\displaystyle lnydy=\frac{1}{2}x^2dx+c$

And I don't quite remember how to integrate a natural log...