\[ y'(x)=\frac {x^4 \sqrt {x^2+y(x)^2}+x y(x)+y(x)}{x (x+1)} \] ✓ Mathematica : cpu = 0.161327 (sec), leaf count = 37
\[\left \{\left \{y(x)\to x \sinh \left (\frac {1}{6} \left (2 x^3-3 x^2+6 x-6 \log (x+1)+11+6 c_1\right )\right )\right \}\right \}\] ✓ Maple : cpu = 1.074 (sec), leaf count = 42
\[ \left \{ \ln \left ( \sqrt { \left ( y \left ( x \right ) \right ) ^{2}+{x}^{2}}+y \left ( x \right ) \right ) -{\frac {{x}^{3}}{3}}+{\frac {{x}^{2}}{2}}-x+\ln \left ( 1+x \right ) -\ln \left ( x \right ) -{\it \_C1}=0 \right \} \]