\[ \boxed { 2\,xy \left ( x \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +2\, \left ( y \left ( x \right ) \right ) ^{2}+1=0} \]
Mathematica: cpu = 0.013502 (sec), leaf count = 60 \[ \left \{\left \{y(x)\to -\frac {\sqrt {e^{4 c_1}-x^2}}{\sqrt {2} x}\right \},\left \{y(x)\to \frac {\sqrt {e^{4 c_1}-x^2}}{\sqrt {2} x}\right \}\right \} \]
Maple: cpu = 0.015 (sec), leaf count = 39 \[ \left \{ y \left ( x \right ) =-{\frac {1}{2\,x}\sqrt {-2\,{x}^{2}+4\,{ \it \_C1}}},y \left ( x \right ) ={\frac {1}{2\,x}\sqrt {-2\,{x}^{2}+4\, {\it \_C1}}} \right \} \]