Solving the differential equation $y' - \frac{1}{x} y = x^2\sqrt{y} $ Which technique should I use for solving the follwoing DE?
$$
y' - \frac{1}{x} y = x^2\sqrt{y}
$$
 I have tried some algebraic manipulations but I could not recognize any pattern.

First, $z=y/x$ yields $z'=x\sqrt{y}=x^{3/2}\sqrt{z}$. 
Then $u=\sqrt{z}$ yields $u'=\frac12x^{3/2}$ hence $u=\frac15x^{5/2}+c$. Finally, $y=xz=xu^2$ hence
$$
y=x\left(\frac15x^{5/2}+c\right)^2.
$$
