$\begin{aligned}
& \frac{d y}{d x}+y\left(\frac{2 x^3+8 x}{\left(x^2+4\right)^2}\right)=\frac{2}{\left(x^2+4\right)^2} \
& \frac{d y}{d x}+y\left(\frac{2 x}{x^2+4}\right)=\frac{2}{\left(x^2+4\right)^2} \
& \text { IF }=e^{\int \frac{2 x}{x^2+4} d x} \
& \text { IF }=x^2+4 \
& y \times\left(x^2+4\right)=\int \frac{2}{\left(x^2+4\right)^2} \times\left(x^2+4\right) \
& y\left(x^2+4\right)=2 \int \frac{d x}{x^2+2^2} \
& y\left(x^2+4\right)=\frac{2}{2} \tan ^{-1}\left(\frac{x}{2}\right)+c \
& 0=0+c=c=0 \
& y\left(x^2+4\right)=\tan ^{-1}\left(\frac{x}{2}\right) \
& y \text { at } x=2 \
& y(4+4)=\tan ^{-1}(1) \
& y(2)=\frac{\pi}{32}
\end{aligned}$