\[ y'(x)=-\frac {x^6}{64}-\frac {3 x^5}{32}+\frac {3}{16} x^4 y(x)-\frac {x^4}{8}+\frac {3}{4} x^3 y(x)+\frac {x^3}{8}-\frac {3}{4} x^2 y(x)^2+\frac {1}{4} x^2 y(x)+\frac {x^2}{4}-\frac {3}{2} x y(x)^2-x y(x)+y(x)^3+y(x)^2+\frac {x}{2}+1 \] ✓ Mathematica : cpu = 0.283358 (sec), leaf count = 102
DSolve[Derivative[1][y][x] == 1 + x/2 + x^2/4 + x^3/8 - x^4/8 - (3*x^5)/32 - x^6/64 - x*y[x] + (x^2*y[x])/4 + (3*x^3*y[x])/4 + (3*x^4*y[x])/16 + y[x]^2 - (3*x*y[x]^2)/2 - (3*x^2*y[x]^2)/4 + y[x]^3,y[x],x]
\[\text {Solve}\left [-\frac {31}{3} \text {RootSum}\left [-31 \text {$\#$1}^3+3\ 2^{2/3} \sqrt [3]{31} \text {$\#$1}-31\& ,\frac {\log \left (\sqrt [3]{\frac {2}{31}} \left (\frac {1}{4} \left (-3 x^2-6 x+4\right )+3 y(x)\right )-\text {$\#$1}\right )}{2^{2/3} \sqrt [3]{31}-31 \text {$\#$1}^2}\& \right ]=\frac {1}{9} \left (\frac {31}{2}\right )^{2/3} x+c_1,y(x)\right ]\] ✓ Maple : cpu = 0.061 (sec), leaf count = 39
dsolve(diff(y(x),x) = 1/2*x+1+y(x)^2+1/4*x^2*y(x)-x*y(x)-1/8*x^4+1/8*x^3+1/4*x^2+y(x)^3-3/4*x^2*y(x)^2-3/2*x*y(x)^2+3/16*y(x)*x^4+3/4*x^3*y(x)-1/64*x^6-3/32*x^5,y(x))
\[y \left (x \right ) = \frac {x^{2}}{4}+\frac {x}{2}+\RootOf \left (-x +2 \left (\int _{}^{\textit {\_Z}}\frac {1}{2 \textit {\_a}^{3}+2 \textit {\_a}^{2}+1}d \textit {\_a} \right )+c_{1}\right )\]