\[ y'(x)=\frac {x^2 \left (-\sqrt {x^2+y(x)^2}\right )+x y(x) \sqrt {x^2+y(x)^2}+x y(x)+y(x)}{x (x+1)} \] ✓ Mathematica : cpu = 0.38423 (sec), leaf count = 239
\[\left \{\left \{y(x)\to \frac {x-2 \sqrt {x^2 \tanh ^2\left (\sqrt {2} x-\sqrt {2} \log (x+1)+\sqrt {2} c_1\right )-x^2 \tanh ^4\left (\sqrt {2} x-\sqrt {2} \log (x+1)+\sqrt {2} c_1\right )}}{-1+2 \tanh ^2\left (\sqrt {2} x-\sqrt {2} \log (x+1)+\sqrt {2} c_1\right )}\right \},\left \{y(x)\to \frac {x+2 \sqrt {x^2 \tanh ^2\left (\sqrt {2} x-\sqrt {2} \log (x+1)+\sqrt {2} c_1\right )-x^2 \tanh ^4\left (\sqrt {2} x-\sqrt {2} \log (x+1)+\sqrt {2} c_1\right )}}{-1+2 \tanh ^2\left (\sqrt {2} x-\sqrt {2} \log (x+1)+\sqrt {2} c_1\right )}\right \}\right \}\] ✓ Maple : cpu = 0.275 (sec), leaf count = 55
\[\left \{-c_{1}+\sqrt {2}\, x -\ln \left (x \right )+\ln \left (\frac {2 \left (x +y \left (x \right )+\sqrt {2 x^{2}+2 y \left (x \right )^{2}}\right ) x}{-x +y \left (x \right )}\right )-\sqrt {2}\, \ln \left (x +1\right ) = 0\right \}\]