We have, $x=\frac{dy}{dx}+2y=x^{2}$
$\Rightarrow \frac{dy}{dx}+\frac{2}{x}\,y=x$
The above equation is a linear differential equation in y.
$\therefore IF=e^{\int \frac{2}{x} dx}\,=e^{2\,log\,x}=x^{2}$
Hence, required solution will be
$ y . x^{2}=\int x . x^{2}\,dx+C_{1}$
$\Rightarrow yx^{2}=\frac{x^{4}}{4}+C_{1}$
$\Rightarrow yx^{2}=\frac{x^{4}+4C_{1}}{4}$
$\Rightarrow y=\frac{x^{4}+C}{4x^{2}}$
$[\because 4C_{1}=C]$