\[ y'(x)=\frac {x^2 \left (-\sqrt {x^2+y(x)^2}\right )+x y(x) \sqrt {x^2+y(x)^2}+x y(x)+y(x)}{x (x+1)} \] ✓ Mathematica : cpu = 0.15672 (sec), leaf count = 109
\[\left \{\left \{y(x)\to \frac {x \left (-2 (x+1)^{\sqrt {2}} e^{\sqrt {2} \left (c_1+x\right )}+e^{2 \sqrt {2} \left (c_1+x\right )}-(x+1)^{2 \sqrt {2}}\right )}{2 (x+1)^{\sqrt {2}} e^{\sqrt {2} \left (c_1+x\right )}+e^{2 \sqrt {2} \left (c_1+x\right )}-(x+1)^{2 \sqrt {2}}}\right \}\right \}\]
✓ Maple : cpu = 0.282 (sec), leaf count = 55
\[ \left \{ \ln \left ( 2\,{\frac {x \left ( \sqrt {2\, \left ( y \left ( x \right ) \right ) ^{2}+2\,{x}^{2}}+y \left ( x \right ) +x \right ) }{y \left ( x \right ) -x}} \right ) +\sqrt {2}x-\ln \left ( x \right ) -\sqrt {2}\ln \left ( 1+x \right ) -{\it \_C1}=0 \right \} \]