Solving the differential equation $(xy^{4}+y)dx - xdy = 0$ The differential equation is : 
$(xy^{4}+y)dx - xdy = 0$
I am trying to simplify the equation to the form $\dfrac{fdg-gdf}{f^{2}}$ so that I can reduce it to $d(\dfrac{g}{f})$ but I am unable to do it.
Any ideas are appreciated.

If you instead let $y(x)=x u(x)$ your differential equation takes the form
$$
\bigl(x(xu)^4+xu)\bigr)\,dx-x(x\,du+u\,dx)=0
$$
that is
$$
x^5u^4\,dx=x^2\,du.
$$
I'm sure you can solve this differential equation.
