\[ y'(x)=\frac {x^5 \left (-\sqrt {x^2+y(x)^2}\right )+x^4 y(x) \sqrt {x^2+y(x)^2}+x y(x)+y(x)}{x (x+1)} \] ✓ Mathematica : cpu = 0.386565 (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 = 0.306 (sec), leaf count = 73
\[ \left \{ \ln \left ( 2\,{\frac {x \left ( \sqrt {2\, \left ( y \left ( x \right ) \right ) ^{2}+2\,{x}^{2}}+y \left ( x \right ) +x \right ) }{y \left ( x \right ) -x}} \right ) +\ln \left ( 1+x \right ) \sqrt {2}+{\frac { \left ( 3\,{x}^{4}-4\,{x}^{3}+6\,{x}^{2}-12\,x \right ) \sqrt {2}}{12}}-{\it \_C1}-\ln \left ( x \right ) =0 \right \} \]