\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =-{\frac {-xy \left ( x \right ) -y \left ( x \right ) +{x}^{5}\sqrt { \left ( y \left ( x \right ) \right ) ^{2}+{x}^{2}}-{x}^{4}\sqrt { \left ( y \left ( x \right ) \right ) ^{2}+{x}^{2}}y \left ( x \right ) }{x \left ( 1+x \right ) }}=0} \]
Mathematica: cpu = 0.293537 (sec), leaf count = 285 \[ \left \{\left \{y(x)\to \frac {x \left (2 (x+1)^{\sqrt {2}} \exp \left (\sqrt {2} c_1+\frac {x^4}{2 \sqrt {2}}+\frac {x^2}{\sqrt {2}}+\frac {1}{3} \sqrt {2} \left (x^2+3\right ) x+\frac {25}{6 \sqrt {2}}\right )+(x+1)^{2 \sqrt {2}} \left (-e^{2 \sqrt {2} c_1+\frac {x^4}{\sqrt {2}}+\sqrt {2} x^2}\right )+e^{\frac {2}{3} \sqrt {2} x \left (x^2+3\right )+\frac {25}{3 \sqrt {2}}}\right )}{-2 (x+1)^{\sqrt {2}} \exp \left (\sqrt {2} c_1+\frac {x^4}{2 \sqrt {2}}+\frac {x^2}{\sqrt {2}}+\frac {1}{3} \sqrt {2} \left (x^2+3\right ) x+\frac {25}{6 \sqrt {2}}\right )+(x+1)^{2 \sqrt {2}} \left (-e^{2 \sqrt {2} c_1+\frac {x^4}{\sqrt {2}}+\sqrt {2} x^2}\right )+e^{\frac {2}{3} \sqrt {2} x \left (x^2+3\right )+\frac {25}{3 \sqrt {2}}}}\right \}\right \} \]
Maple: cpu = 0.187 (sec), leaf count = 79 \[ \left \{ \ln \left ( 2\,{\frac {x \left ( \sqrt {2\, \left ( y \left ( x \right ) \right ) ^{2}+2\,{x}^{2}}+y \left ( x \right ) +x \right ) }{y \left ( x \right ) -x}} \right ) +{\frac {\sqrt {2}{x}^{4}}{4}}-{\frac { \sqrt {2}{x}^{3}}{3}}+{\frac {\sqrt {2}{x}^{2}}{2}}-x\sqrt {2}-\ln \left ( x \right ) +\sqrt {2}\ln \left ( 1+x \right ) -{\it \_C1}=0 \right \} \]