\[ y'(x)=\frac {x^4 \sqrt {x^2+y(x)^2}+x y(x)+y(x)}{x (x+1)} \] ✓ Mathematica : cpu = 0.190937 (sec), leaf count = 88
DSolve[Derivative[1][y][x] == (y[x] + x*y[x] + x^4*Sqrt[x^2 + y[x]^2])/(x*(1 + x)),y[x],x]
\[\left \{\left \{y(x)\to \frac {x e^{-\frac {x^3}{3}-\frac {x^2}{2}-x-\frac {11}{6}-c_1} \left (e^{\frac {2 x^3}{3}+2 x+\frac {11}{3}+2 c_1}-e^{x^2} x^2-2 e^{x^2} x-e^{x^2}\right )}{2 (x+1)}\right \}\right \}\] ✓ Maple : cpu = 1.707 (sec), leaf count = 42
dsolve(diff(y(x),x) = (x*y(x)+y(x)+x^4*(y(x)^2+x^2)^(1/2))/x/(1+x),y(x))
\[\ln \left (\sqrt {y \left (x \right )^{2}+x^{2}}+y \left (x \right )\right )-\frac {x^{3}}{3}+\frac {x^{2}}{2}-x +\ln \left (1+x \right )-\ln \left (x \right )-c_{1} = 0\]