\[ y'(x)=\frac {x^5 \left (-\sqrt {x^2+y(x)^2}\right )+x^4 y(x) \sqrt {x^2+y(x)^2}+x y(x)+y(x)}{x (x+1)} \] ✓ Mathematica : cpu = 0.300839 (sec), leaf count = 497
\[\left \{\left \{y(x)\to \frac {x-2 \sqrt {x^2 \tanh ^2\left (\frac {1}{12} \left (-3 \sqrt {2} x^4+4 \sqrt {2} x^3-6 \sqrt {2} x^2+12 \sqrt {2} x-12 \sqrt {2} \log (x+1)+25 \sqrt {2}-12 \sqrt {2} c_1\right )\right )-x^2 \tanh ^4\left (\frac {1}{12} \left (-3 \sqrt {2} x^4+4 \sqrt {2} x^3-6 \sqrt {2} x^2+12 \sqrt {2} x-12 \sqrt {2} \log (x+1)+25 \sqrt {2}-12 \sqrt {2} c_1\right )\right )}}{-1+2 \tanh ^2\left (\frac {1}{12} \left (-3 \sqrt {2} x^4+4 \sqrt {2} x^3-6 \sqrt {2} x^2+12 \sqrt {2} x-12 \sqrt {2} \log (x+1)+25 \sqrt {2}-12 \sqrt {2} c_1\right )\right )}\right \},\left \{y(x)\to \frac {x+2 \sqrt {x^2 \tanh ^2\left (\frac {1}{12} \left (-3 \sqrt {2} x^4+4 \sqrt {2} x^3-6 \sqrt {2} x^2+12 \sqrt {2} x-12 \sqrt {2} \log (x+1)+25 \sqrt {2}-12 \sqrt {2} c_1\right )\right )-x^2 \tanh ^4\left (\frac {1}{12} \left (-3 \sqrt {2} x^4+4 \sqrt {2} x^3-6 \sqrt {2} x^2+12 \sqrt {2} x-12 \sqrt {2} \log (x+1)+25 \sqrt {2}-12 \sqrt {2} c_1\right )\right )}}{-1+2 \tanh ^2\left (\frac {1}{12} \left (-3 \sqrt {2} x^4+4 \sqrt {2} x^3-6 \sqrt {2} x^2+12 \sqrt {2} x-12 \sqrt {2} \log (x+1)+25 \sqrt {2}-12 \sqrt {2} c_1\right )\right )}\right \}\right \}\] ✓ Maple : cpu = 0.238 (sec), leaf count = 73
\[\left \{-c_{1}-\ln \left (x \right )+\ln \left (\frac {2 \left (x +y \left (x \right )+\sqrt {2 x^{2}+2 y \left (x \right )^{2}}\right ) x}{-x +y \left (x \right )}\right )+\sqrt {2}\, \ln \left (x +1\right )+\frac {\left (3 x^{4}-4 x^{3}+6 x^{2}-12 x \right ) \sqrt {2}}{12} = 0\right \}\]