\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={1 \left ( \left ( y \left ( x \right ) \right ) ^{2}+2\,xy \left ( x \right ) +{x}^{2}+{{\rm e}^{-2\, \left ( - \left ( y \left ( x \right ) \right ) ^{2}+{x}^{2}-1 \right ) ^{-1}}} \right ) \left ( \left ( y \left ( x \right ) \right ) ^{2}+2\,xy \left ( x \right ) +{x}^{2}-{{\rm e}^{-2\, \left ( - \left ( y \left ( x \right ) \right ) ^{2}+{x}^{2}-1 \right ) ^{-1}}} \right ) ^{-1}}=0} \]
Mathematica: cpu = 0 (sec), leaf count = 0 \[ \text {Hanged} \]
Maple: cpu = 0.452 (sec), leaf count = 40 \[ \left \{ y \left ( x \right ) ={{\rm e}^{{\it RootOf} \left ( -{\it \_Z}+ \int ^{ \left ( {{\rm e}^{{\it \_Z}}} \right ) ^{2}-2\,x{{\rm e}^{{\it \_Z}}}}\! \left ( {{\rm e}^{2\, \left ( {\it \_a}+1 \right ) ^{-1}}}+{ \it \_a} \right ) ^{-1}{d{\it \_a}}+{\it \_C1} \right ) }}-x \right \} \]