Let y=y(x) be the solution of the differential equation

Let $\mathbf{y}+1=\mathrm{Y}$

$\therefore \frac{\mathrm{d} \mathrm{Y}}{\mathrm{dx}}=\mathrm{Y}^{2} \mathrm{e}^{\frac{x^{2}}{2}}-\mathrm{x} \mathrm{Y}$

Put $-\frac{1}{Y}=k$

$\Rightarrow \frac{\mathrm{dk}}{\mathrm{dx}}+\mathrm{k}(-\mathrm{x})=\mathrm{e}^{\frac{\mathrm{x}^{2}}{2}}$

I.F. $=\mathrm{e}^{-\frac{x^{2}}{2}}$

$\therefore \mathrm{k}=(\mathrm{x}+\mathrm{c}) \mathrm{e}^{\mathrm{x}^{2} / 2}$

Put $k=-\frac{1}{y+1}$

$\therefore y+1=-\frac{1}{(x+c) e^{x^{2} / 2}}$

when $x=2, y=0$, then $c=-2-\frac{1}{e^{2}}$

diffentiate equation

(i) \& put $x=1$

we get $\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)_{\mathrm{x}=1}=-\frac{\mathrm{e}^{3 / 2}}{\left(1+\mathrm{e}^{2}\right)^{2}}$