\[ y'(x)=x^2 \sqrt {x^2+8 y(x)-2 x+1}+\sqrt {x^2+8 y(x)-2 x+1}+x^3 \sqrt {x^2+8 y(x)-2 x+1}-\frac {x}{4}+\frac {1}{4} \] ✓ Mathematica : cpu = 0.38341 (sec), leaf count = 69
\[\left \{\left \{y(x)\to \frac {1}{72} \left (-72 c_1 x^4-96 c_1 x^3-288 c_1 x+144 c_1^2+9 x^8+24 x^7+16 x^6+72 x^5+96 x^4+135 x^2+18 x-9\right )\right \}\right \}\] ✓ Maple : cpu = 0.331 (sec), leaf count = 32
\[ \left \{ {\it \_C1}+{x}^{4}+{\frac {4\,{x}^{3}}{3}}+4\,x-\sqrt {{x}^{2}-2\,x+1+8\,y \left ( x \right ) }=0 \right \} \]