\[ y'(x)=\frac {x^6 \sqrt {4 x^2 y(x)+1}+\frac {x}{2}+\frac {1}{2}}{x^3 (x+1)} \] ✓ Mathematica : cpu = 0.434449 (sec), leaf count = 144
DSolve[Derivative[1][y][x] == (1/2 + x/2 + x^6*Sqrt[1 + 4*x^2*y[x]])/(x^3*(1 + x)),y[x],x]
\[\left \{\left \{y(x)\to \frac {9 x^{10}-24 x^9+52 x^8-120 x^7+132 x^6+72 x^6 \log (x+1)-72 c_1 x^6-144 x^5-96 x^5 \log (x+1)+96 c_1 x^5+144 x^4+144 x^4 \log (x+1)-144 c_1 x^4-288 x^3 \log (x+1)+288 c_1 x^3+144 x^2 \log ^2(x+1)+144 c_1{}^2 x^2-288 c_1 x^2 \log (x+1)-36}{144 x^2}\right \}\right \}\] ✓ Maple : cpu = 0.644 (sec), leaf count = 43
dsolve(diff(y(x),x) = 1/2*(x+1+2*x^6*(4*x^2*y(x)+1)^(1/2))/x^3/(1+x),y(x))
\[c_{1}+2 \ln \left (1+x \right )-\frac {\sqrt {4 x^{2} y \left (x \right )+1}}{x}-2 x +x^{2}-\frac {2 x^{3}}{3}+\frac {x^{4}}{2} = 0\]