The differential equation $x\frac{dy}{dx} -y =x^2$, has the general solution

$2y-x^3=Cx$

The correct answer is option (2) : $2y-x^3=Cx$

We have,

$\frac{dy}{dx} + \left(-\frac{1}{x}\right) y = x^2$

It is a linear differential equation with integrating factor

$I.F.=e^{∫-\frac{1}{x}dx}=e^{-log\, x}=\frac{1}{x}$

Multiplying (i) by $\frac{1}{x}$ and integrating, we get

$\frac{y}{x}=\frac{x^2}{2}+C$ or , $2y-x^3=2Cx$