\[ y'(x)=\frac {x^6}{512}-\frac {3 x^5}{256}+\frac {3}{64} x^4 y(x)+\frac {5 x^4}{128}-\frac {3}{16} x^3 y(x)-\frac {5 x^3}{64}+\frac {3}{8} x^2 y(x)^2+\frac {7}{16} x^2 y(x)+\frac {x^2}{16}-\frac {3}{4} x y(x)^2-\frac {1}{2} x y(x)+y(x)^3+y(x)^2-\frac {x}{4}+1 \] ✓ Mathematica : cpu = 0.265812 (sec), leaf count = 99
DSolve[Derivative[1][y][x] == 1 - x/4 + x^2/16 - (5*x^3)/64 + (5*x^4)/128 - (3*x^5)/256 + x^6/512 - (x*y[x])/2 + (7*x^2*y[x])/16 - (3*x^3*y[x])/16 + (3*x^4*y[x])/64 + y[x]^2 - (3*x*y[x]^2)/4 + (3*x^2*y[x]^2)/8 + y[x]^3,y[x],x]
\[\text {Solve}\left [-\frac {89}{3} \text {RootSum}\left [-89 \text {$\#$1}^3+6 \sqrt [3]{178} \text {$\#$1}-89\& ,\frac {\log \left (\frac {2^{2/3} \left (\frac {1}{8} \left (3 x^2-6 x+8\right )+3 y(x)\right )}{\sqrt [3]{89}}-\text {$\#$1}\right )}{2 \sqrt [3]{178}-89 \text {$\#$1}^2}\& \right ]=\frac {89^{2/3} x}{18 \sqrt [3]{2}}+c_1,y(x)\right ]\] ✓ Maple : cpu = 0.062 (sec), leaf count = 39
dsolve(diff(y(x),x) = -1/4*x+1+y(x)^2+7/16*x^2*y(x)-1/2*x*y(x)+5/128*x^4-5/64*x^3+1/16*x^2+y(x)^3+3/8*x^2*y(x)^2-3/4*x*y(x)^2+3/64*y(x)*x^4-3/16*x^3*y(x)+1/512*x^6-3/256*x^5,y(x))
\[y \left (x \right ) = -\frac {x^{2}}{8}+\frac {x}{4}+\RootOf \left (-x +4 \left (\int _{}^{\textit {\_Z}}\frac {1}{4 \textit {\_a}^{3}+4 \textit {\_a}^{2}+3}d \textit {\_a} \right )+c_{1}\right )\]