The solution of the differential equation dy/dx-y/x=x^3 is

\(\frac{dy}{dx}-\frac{y}{x}=x^3\)

so $\int \frac{1}{x}\frac{dy}{dx}-\frac{ydx}{x^2}=\int x^2dx$

$\frac{y}{x}=\frac{x^3}{3}+\frac{C}{3}⇒3y=x(x^3+c)$