\[ y'(x)=\frac {-\frac {x^2}{4}+x^3 \sqrt {x^2+8 y(x)-2 x+1}+\frac {1}{4}}{x+1} \] ✓ Mathematica : cpu = 0.508206 (sec), leaf count = 105
DSolve[Derivative[1][y][x] == (1/4 - x^2/4 + x^3*Sqrt[1 - 2*x + x^2 + 8*y[x]])/(1 + x),y[x],x]
\[\left \{\left \{y(x)\to \frac {1}{72} \left (16 x^6-48 x^5+132 x^4-144 x^3-96 x^3 \log (x+1)-96 c_1 x^3+135 x^2+144 x^2 \log (x+1)+144 c_1 x^2+18 x+144 \log ^2(x+1)-288 x \log (x+1)-288 c_1 x+288 c_1 \log (x+1)-9+144 c_1{}^2\right )\right \}\right \}\] ✓ Maple : cpu = 0.533 (sec), leaf count = 40
dsolve(diff(y(x),x) = 1/4*(-x^2+1+4*x^3*(x^2-2*x+1+8*y(x))^(1/2))/(1+x),y(x))
\[c_{1}+\frac {4 x^{3}}{3}-2 x^{2}+4 x -4 \ln \left (1+x \right )-\sqrt {x^{2}-2 x +1+8 y \left (x \right )} = 0\]