\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {xy \left ( x \right ) +y \left ( x \right ) +x\sqrt { \left ( y \left ( x \right ) \right ) ^{2}+{x}^{2}}}{x \left ( 1+x \right ) }}=0} \]
Mathematica: cpu = 0.023003 (sec), leaf count = 15 \[ \left \{\left \{y(x)\to x \sinh \left (c_1+\log (x+1)\right )\right \}\right \} \]
Maple: cpu = 0.280 (sec), leaf count = 27 \[ \left \{ {\it \_C1}+{\frac {1}{x \left ( 1+x \right ) } \left ( \sqrt { \left ( y \left ( x \right ) \right ) ^{2}+{x}^{2}}+y \left ( x \right ) \right ) }=0 \right \} \]