\[ y'(x)=\frac {\sqrt {x^2-4 y(x)+2 x+1}+\frac {x^2}{2}+x+\frac {1}{2}}{x+1} \] ✓ Mathematica : cpu = 0.317045 (sec), leaf count = 39
DSolve[Derivative[1][y][x] == (1/2 + x + x^2/2 + Sqrt[1 + 2*x + x^2 - 4*y[x]])/(1 + x),y[x],x]
\[\left \{\left \{y(x)\to \frac {1}{4} \left (x^2+2 x-4 \log ^2(x+1)+8 c_1 \log (x+1)+1-4 c_1{}^2\right )\right \}\right \}\] ✓ Maple : cpu = 0.333 (sec), leaf count = 28
dsolve(diff(y(x),x) = 1/2*(x^2+2*x+1+2*(x^2+2*x+1-4*y(x))^(1/2))/(1+x),y(x))
\[c_{1}-2 \ln \left (1+x \right )-\frac {1}{2}-\sqrt {x^{2}+2 x +1-4 y \left (x \right )} = 0\]