Find general solution to the equation $xy^{'}=2x^2\sqrt{y}+4y$ This is Bernoulli's differential equation:
$$xy^{'}-4y=2x^2y^{\frac{1}{2}}$$
Substitution $y=z^{\frac{1}{1-\alpha}},\alpha=\frac{1}{2},y^{'}=z^{'2}$ gives $$xz^{'2}-4z^2=2x^2z$$
Is this correct? What is the method for solving this equation?

If y = z^2 ... when you differentiate this equation with respect to x ... notice z is implicitly dependant on x too. So take this into account.
Hint: Chain rule
