dy/dx - 2y = (4x)/(y^1/2)
I assumed that u = y^1/2 would be the proper substitution, but it didn't seem like things were going in the right direction.
The substitution is of the form , so we see in this case, the proper substitution would be
Try to take it from here. This should lead you to the desired result.
See here for an example on how to solve a Bernoulli equation (see post #3)
I hope this helps!