\[ y'(x)=\frac {x^3 \sqrt {4 x^2 y(x)+1}+\frac {x}{2}+\frac {1}{2}}{x^3 (x+1)} \] ✓ Mathematica : cpu = 0.587036 (sec), leaf count = 64
DSolve[Derivative[1][y][x] == (1/2 + x/2 + x^3*Sqrt[1 + 4*x^2*y[x]])/(x^3*(1 + x)),y[x],x]
\[\left \{\left \{y(x)\to x^2-\frac {1}{4 x^2}+\frac {1}{4} \log ^2\left (x^2+2 x+1\right )-x \log \left (x^2+2 x+1\right )+c_1 \log \left (x^2+2 x+1\right )-2 c_1 x+c_1{}^2\right \}\right \}\] ✓ Maple : cpu = 0.5 (sec), leaf count = 30
dsolve(diff(y(x),x) = 1/2*(x+1+2*(4*x^2*y(x)+1)^(1/2)*x^3)/x^3/(1+x),y(x))
\[-2 \ln \left (1+x \right )-\frac {\sqrt {4 x^{2} y \left (x \right )+1}}{x}+2 x +c_{1} = 0\]