\[ y'(x)=\frac {x^5 \left (-\sqrt {x^2+y(x)^2}\right )+x^4 y(x) \sqrt {x^2+y(x)^2}+x y(x)+y(x)}{x (x+1)} \] ✓ Mathematica : cpu = 0.256636 (sec), leaf count = 497
DSolve[Derivative[1][y][x] == (y[x] + x*y[x] - x^5*Sqrt[x^2 + y[x]^2] + x^4*y[x]*Sqrt[x^2 + y[x]^2])/(x*(1 + x)),y[x],x]
\[\left \{\left \{y(x)\to \frac {x-2 \sqrt {x^2 \tanh ^2\left (\frac {1}{12} \left (-3 \sqrt {2} x^4+4 \sqrt {2} x^3-6 \sqrt {2} x^2+12 \sqrt {2} x-12 \sqrt {2} \log (x+1)+25 \sqrt {2}-12 \sqrt {2} c_1\right )\right )-x^2 \tanh ^4\left (\frac {1}{12} \left (-3 \sqrt {2} x^4+4 \sqrt {2} x^3-6 \sqrt {2} x^2+12 \sqrt {2} x-12 \sqrt {2} \log (x+1)+25 \sqrt {2}-12 \sqrt {2} c_1\right )\right )}}{-1+2 \tanh ^2\left (\frac {1}{12} \left (-3 \sqrt {2} x^4+4 \sqrt {2} x^3-6 \sqrt {2} x^2+12 \sqrt {2} x-12 \sqrt {2} \log (x+1)+25 \sqrt {2}-12 \sqrt {2} c_1\right )\right )}\right \},\left \{y(x)\to \frac {x+2 \sqrt {x^2 \tanh ^2\left (\frac {1}{12} \left (-3 \sqrt {2} x^4+4 \sqrt {2} x^3-6 \sqrt {2} x^2+12 \sqrt {2} x-12 \sqrt {2} \log (x+1)+25 \sqrt {2}-12 \sqrt {2} c_1\right )\right )-x^2 \tanh ^4\left (\frac {1}{12} \left (-3 \sqrt {2} x^4+4 \sqrt {2} x^3-6 \sqrt {2} x^2+12 \sqrt {2} x-12 \sqrt {2} \log (x+1)+25 \sqrt {2}-12 \sqrt {2} c_1\right )\right )}}{-1+2 \tanh ^2\left (\frac {1}{12} \left (-3 \sqrt {2} x^4+4 \sqrt {2} x^3-6 \sqrt {2} x^2+12 \sqrt {2} x-12 \sqrt {2} \log (x+1)+25 \sqrt {2}-12 \sqrt {2} c_1\right )\right )}\right \}\right \}\] ✓ Maple : cpu = 0.21 (sec), leaf count = 73
dsolve(diff(y(x),x) = -(-x*y(x)-y(x)+x^5*(y(x)^2+x^2)^(1/2)-x^4*(y(x)^2+x^2)^(1/2)*y(x))/x/(1+x),y(x))
\[\ln \left (\frac {2 x \left (\sqrt {2 y \left (x \right )^{2}+2 x^{2}}+y \left (x \right )+x \right )}{y \left (x \right )-x}\right )+\sqrt {2}\, \ln \left (1+x \right )+\frac {\left (3 x^{4}-4 x^{3}+6 x^{2}-12 x \right ) \sqrt {2}}{12}-c_{1}-\ln \left (x \right ) = 0\]