\[ y'(x)=\frac {\sqrt {x^2+8 y(x)-2 x+1}-\frac {x^2}{4}+\frac {1}{4}}{x+1} \] ✓ Mathematica : cpu = 0.417135 (sec), leaf count = 41
DSolve[Derivative[1][y][x] == (1/4 - x^2/4 + Sqrt[1 - 2*x + x^2 + 8*y[x]])/(1 + x),y[x],x]
\[\left \{\left \{y(x)\to \frac {1}{8} \left (-x^2+2 x+16 \log ^2(x+1)-32 c_1 \log (x+1)-1+16 c_1{}^2\right )\right \}\right \}\] ✓ Maple : cpu = 0.462 (sec), leaf count = 28
dsolve(diff(y(x),x) = -1/4*(x^2-1-4*(x^2-2*x+1+8*y(x))^(1/2))/(1+x),y(x))
\[c_{1}+4 \ln \left (1+x \right )-\frac {1}{4}-\sqrt {x^{2}-2 x +1+8 y \left (x \right )} = 0\]