Consider the differential equation,

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

$\frac{d x}{d y}+\frac{x}{y^{2}}=\frac{1}{y^{3}}$

$I F=e^{\int \frac{1}{y^{2}} d y}=e^{-\frac{1}{y}}$

$e^{-\frac{1}{y}} \cdot x=\int e^{-\frac{1}{y}} \cdot \frac{1}{y^{3}} d y+C$

$x e^{-\frac{1}{y}}=e^{-\frac{1}{y}}+\frac{e^{-\frac{1}{y}}}{y}+C$

$\mathrm{C}=-\frac{1}{\mathrm{e}}$

$x=\frac{3}{2}-\frac{1}{\sqrt{\mathrm{e}}}$ when $y=2$