\[ \boxed { \left ( 6\,y \left ( x \right ) -x \right ) ^{2}{\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -6\, \left ( y \left ( x \right ) \right ) ^{2}+2\,xy \left ( x \right ) +a=0} \]
Mathematica: cpu = 0.016502 (sec), leaf count = 115 \[ \left \{\left \{y(x)\to \frac {1}{6} \left (\sqrt [3]{-18 a x+18 c_1-x^3}+x\right )\right \},\left \{y(x)\to \frac {x}{6}-\frac {1}{12} \left (1-i \sqrt {3}\right ) \sqrt [3]{-18 a x+18 c_1-x^3}\right \},\left \{y(x)\to \frac {x}{6}-\frac {1}{12} \left (1+i \sqrt {3}\right ) \sqrt [3]{-18 a x+18 c_1-x^3}\right \}\right \} \]
Maple: cpu = 0.031 (sec), leaf count = 115 \[ \left \{ y \left ( x \right ) ={\frac {1}{6}\sqrt [3]{-{x}^{3}-18\,ax-18 \,{\it \_C1}}}+{\frac {x}{6}},y \left ( x \right ) =-{\frac {1}{12} \sqrt [3]{-{x}^{3}-18\,ax-18\,{\it \_C1}}}-{\frac {i}{12}}\sqrt {3} \sqrt [3]{-{x}^{3}-18\,ax-18\,{\it \_C1}}+{\frac {x}{6}},y \left ( x \right ) =-{\frac {1}{12}\sqrt [3]{-{x}^{3}-18\,ax-18\,{\it \_C1}}}+{ \frac {i}{12}}\sqrt {3}\sqrt [3]{-{x}^{3}-18\,ax-18\,{\it \_C1}}+{ \frac {x}{6}} \right \} \]