The differential equation x (d y)/(d x)-y=x^2, has the general soluti…

$\frac{xd y}{d x}-y=x^2$

so $\frac{xdy-ydx}{x^2}=dx$

so $\int d(\frac{y}{x})=\int dx$

so $\frac{y}{x}=x+C$

so $y=x^2+Cx$

so $y-x^2=Cx$