There is a fairly storng hint to use part a), but you go wrong from line 1 to line 2 (basic algebra). If you take 3sqrt(y) over, its -3sqrt(y) + dy/dx on the left, which isnt useful for this approach. You have multiply/divide by a term to attach it to dy/dx on the left.
Edit - when you do seperation of variables you essentially want to get a "reverse chain rule" on the left. Your basic equation should be something like
f(y) dy/dx = g(x)
where you know y is a function of x so y(x).
If jump ahead and imagine the integral of that (whatever it is) to be
F(y) = G(x)
then differentiating both sides with respect to x (chain rule on the left) you get
dF/dy dy/dx = dG/dx
so
f = dF/dy
g = dG/dx
Note that the dF/dy term must be multipied by dy/dx. Treating integration as reverse differentiation, then the integral of f(y) dy/dx with respect to x is simply the integral of f(y) with respect to y.