\[ y'(x)=x^2 \sqrt {x^2+8 y(x)-2 x+1}+\sqrt {x^2+8 y(x)-2 x+1}+x^3 \sqrt {x^2+8 y(x)-2 x+1}-\frac {x}{4}+\frac {1}{4} \] ✓ Mathematica : cpu = 0.393899 (sec), leaf count = 69
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]
\[\left \{\left \{y(x)\to \frac {1}{72} \left (9 x^8+24 x^7+16 x^6+72 x^5+96 x^4-72 c_1 x^4-96 c_1 x^3+135 x^2+18 x-288 c_1 x-9+144 c_1{}^2\right )\right \}\right \}\] ✓ Maple : cpu = 0.388 (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))
\[c_{1}+x^{4}+\frac {4 x^{3}}{3}+4 x -\sqrt {x^{2}-2 x +1+8 y \left (x \right )} = 0\]