The integrating factor of the differential equation

The given differential equation is:

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

$\Rightarrow \frac{d y}{d x}-\frac{y}{x}=2 x$

This is a linear differential equation of the form:

$\frac{d y}{d x}+p y=Q\left(\right.$ where $p=-\frac{1}{x}$ and $\left.Q=2 x\right)$

$e^{\int p d x}$

$\therefore$ I.F $=e^{\int-\frac{1}{x} d x}=e^{-\log x}=e^{\log \left(x^{-1}\right)}=x^{-1}=\frac{1}{x}$

Hence, the correct answer is C.