\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {2\,{x}^{2}+2\,x+{x}^{4}-2\,{x}^{2}y \left ( x \right ) -1+ \left ( y \left ( x \right ) \right ) ^{2}}{1+x}}=0} \]
Mathematica: cpu = 0.106514 (sec), leaf count = 31 \[ \left \{\left \{y(x)\to \frac {(x+1)^2}{c_1-\frac {x^2}{2}-x}+x^2+1\right \}\right \} \]
Maple: cpu = 0.140 (sec), leaf count = 47 \[ \left \{ y \left ( x \right ) ={\frac {{\it \_C1}\,{x}^{4}+2\,{\it \_C1} \,{x}^{3}-{x}^{2}{\it \_C1}-2\,{\it \_C1}\,x+{x}^{2}-2\,{\it \_C1}+1}{ {x}^{2}{\it \_C1}+2\,{\it \_C1}\,x+1}} \right \} \]