\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {xy \left ( x \right ) +y \left ( x \right ) +{x}^{4}\sqrt { \left ( y \left ( x \right ) \right ) ^{2}+{x}^{2}}}{x \left ( 1+x \right ) }}=0} \]
Mathematica: cpu = 0.055507 (sec), leaf count = 37 \[ \left \{\left \{y(x)\to x \sinh \left (\frac {1}{6} \left (6 c_1+2 x^3-3 x^2+6 x-6 \log (x+1)+11\right )\right )\right \}\right \} \]
Maple: cpu = 0.422 (sec), leaf count = 42 \[ \left \{ \ln \left ( y \left ( x \right ) +\sqrt { \left ( y \left ( x \right ) \right ) ^{2}+{x}^{2}} \right ) -{\frac {{x}^{3}}{3}}+{\frac { {x}^{2}}{2}}-x-\ln \left ( x \right ) +\ln \left ( 1+x \right ) -{\it \_C1}=0 \right \} \]