\[ y'(x)=x^2 \sqrt {x^2+8 y(x)-2 x+1}+\sqrt {x^2+8 y(x)-2 x+1}+x^3 \sqrt {x^2+8 y(x)-2 x+1}-\frac {x}{4}+\frac {1}{4} \] ✓ Mathematica : cpu = 0.803014 (sec), leaf count = 107
DSolve[Derivative[1][y][x] == 1/4 - x/4 + Sqrt[1 - 2*x + x^2 + 8*y[x]] + x^2*Sqrt[1 - 2*x + x^2 + 8*y[x]] + x^3*Sqrt[1 - 2*x + x^2 + 8*y[x]],y[x],x]
\[\text {Solve}\left [\frac {x^4}{4}+\frac {x^3}{3}-\frac {1}{4} \sqrt {x^2+8 y(x)-2 x+1}+\frac {1}{4} \log \left (-\sqrt {x^2+8 y(x)-2 x+1}-x+1\right )-\frac {1}{4} \tanh ^{-1}\left (\frac {2 x-2}{2 \sqrt {x^2+8 y(x)-2 x+1}}\right )-\frac {1}{8} \log (y(x))+x=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.352 (sec), leaf count = 32
dsolve(diff(y(x),x) = -1/4*x+1/4+(x^2-2*x+1+8*y(x))^(1/2)+x^2*(x^2-2*x+1+8*y(x))^(1/2)+x^3*(x^2-2*x+1+8*y(x))^(1/2),y(x))
\[c_{1}+x^{4}+\frac {4 x^{3}}{3}+4 x -\sqrt {x^{2}-2 x +1+8 y \left (x \right )} = 0\]