\[ y'(x)=\frac {x^2 \left (-\sqrt {x^2+y(x)^2}\right )+x y(x) \sqrt {x^2+y(x)^2}+x y(x)+y(x)}{x (x+1)} \] ✓ Mathematica : cpu = 0.329682 (sec), leaf count = 239
DSolve[Derivative[1][y][x] == (y[x] + x*y[x] - x^2*Sqrt[x^2 + y[x]^2] + x*y[x]*Sqrt[x^2 + y[x]^2])/(x*(1 + x)),y[x],x]
\[\left \{\left \{y(x)\to \frac {x-2 \sqrt {x^2 \tanh ^2\left (\sqrt {2} x-\sqrt {2} \log (x+1)+\sqrt {2} c_1\right )-x^2 \tanh ^4\left (\sqrt {2} x-\sqrt {2} \log (x+1)+\sqrt {2} c_1\right )}}{-1+2 \tanh ^2\left (\sqrt {2} x-\sqrt {2} \log (x+1)+\sqrt {2} c_1\right )}\right \},\left \{y(x)\to \frac {x+2 \sqrt {x^2 \tanh ^2\left (\sqrt {2} x-\sqrt {2} \log (x+1)+\sqrt {2} c_1\right )-x^2 \tanh ^4\left (\sqrt {2} x-\sqrt {2} \log (x+1)+\sqrt {2} c_1\right )}}{-1+2 \tanh ^2\left (\sqrt {2} x-\sqrt {2} \log (x+1)+\sqrt {2} c_1\right )}\right \}\right \}\] ✓ Maple : cpu = 0.196 (sec), leaf count = 55
dsolve(diff(y(x),x) = -(-x*y(x)-y(x)+(y(x)^2+x^2)^(1/2)*x^2-x*(y(x)^2+x^2)^(1/2)*y(x))/x/(1+x),y(x))
\[\ln \left (\frac {2 x \left (\sqrt {2 y \left (x \right )^{2}+2 x^{2}}+y \left (x \right )+x \right )}{y \left (x \right )-x}\right )+\sqrt {2}\, x -\ln \left (x \right )-\sqrt {2}\, \ln \left (1+x \right )-c_{1} = 0\]