\[ a+(6 y(x)-x)^2 y'(x)-6 y(x)^2+2 x y(x)=0 \] ✓ Mathematica : cpu = 0.187592 (sec), leaf count = 115
\[\left \{\left \{y(x)\to \frac {1}{6} \left (x+\sqrt [3]{-18 a x-x^3+18 c_1}\right )\right \},\left \{y(x)\to \frac {x}{6}-\frac {1}{12} \left (1-i \sqrt {3}\right ) \sqrt [3]{-18 a x-x^3+18 c_1}\right \},\left \{y(x)\to \frac {x}{6}-\frac {1}{12} \left (1+i \sqrt {3}\right ) \sqrt [3]{-18 a x-x^3+18 c_1}\right \}\right \}\] ✓ Maple : cpu = 0.04 (sec), leaf count = 115
\[y \relax (x ) = \frac {\left (-x^{3}-18 a x -18 c_{1}\right )^{\frac {1}{3}}}{6}+\frac {x}{6}\]