Find the solution for differential equation $x^2(dy/dx) + 2xy = y^3$

Question

I tried solving this by bernoulli type , but coefficient didn't came appropriate.

Answer 1

Divide by $y^2$ to get $\frac{x^2}{y^3}\frac{dy}{dx}+\frac{2x}{y^2}=1$.

Substitute $\frac{1}{y^2}=z$ which gives $\frac{1}{y^3}\frac{dy}{dx} =\frac{-1}{2}\frac{dz}{dx}$ to get Linear differential equation

$\frac{dz}{dx}-\frac{4}{x}z=\frac{-2}{x^2}$ which you can solve.