Question

Solve the equation: (x^4 - x + y)dx - xdy=0

Answer 1

Keeping in mind that "dx" is the delta x, or differential over the x-axis, whilst "dy" is the delta y or differential over the y-axis,

$\bf (x^4-x+y)dx-xdy=0\implies \stackrel{\textit{distributing dx}}{x^4dx-xdx+ydx}-xdy=0 \\\\\\ ydx=xdy-x^4dx+xdx\implies y=\cfrac{xdy-x^4dx+xdx}{dx} \\\\\\ y=\stackrel{\textit{distributing the denominator}}{x\cfrac{dy}{dx}-x^4+x}$